Cho mặt cầu [S] tâm O, bán kính R và mặt phẳng [P] có khoảng cách đến Obằng R. M là một điểm tùy ý thuộc [S]. Đường thẳng OM cắt [P] tại N. Hìnhchiếu của O trên [P] là I.Mệnh đề nào sau đây đúng?
A. NI tiếp xúc với [S].
B. ON = R
C. "NI tiếp xúc với [S]" và "ON = R
D. "NI tiếp xúc với [S]" và "ON = R
Đáp án và lời giải
Đáp án:D
Lời giải:
+ Vì I là hình chiếu của O trên [P] nênd [O , [P]] = OImà d[O , [P]] = Rnên I là tiếp điểm của [P] và [S].
+ Đường thẳng OM cắt [P ] tại N nên INvuông góc với OI tại I . Suy ra NI tiếp xúc với [S].
+ Tam giác OIN vuông tại I nên ON = R
Câu hỏi thuộc đề thi sau. Bạn có muốn thi thử?
Trắc nghiệm Toán 12 Phần Hình học Chương 2 Mặt Nón, Mặt Trụ, Mặt Cầu 20 phút - Đề số 5
Làm bài
Chia sẻ
Một số câu hỏi khác cùng bài thi.
-
Cho tam giác ABC có I là trung điểm của BC. Vẽ ra ngoài tam giác đó haitam giác ACE và ABF vuông cân tại A . Đặt AF = a và
=α . GọiJ = EF ∩AI . Cho hình vẽ quay quanh đường thẳng AI cố định.Điểm J trùng với điểm nào sau đây của tam giác AFE ? -
Cho mặt phẳng [α] và hai điểm cố định A và B thuộc [α]. M là điểmdi động trong không gian có hình chiếu trên[α] là I. Gọi O là trung điểm của AB,Δ vuông góc với[α] tại O. Tập hợp những điểm M khi
là: -
Cho mặt cầu [S] tâm O, bán kính R và mặt phẳng [P] có khoảng cách đến Obằng R. M là một điểm tùy ý thuộc [S]. Đường thẳng OM cắt [P] tại N. Hìnhchiếu của O trên [P] là I.Mệnh đề nào sau đây đúng?
-
Câu nào sau đây sai?
-
Cho tam giác ABC có I là trung điểm của BC. Vẽ ra ngoài tam giác đó haitam giác ACE và ABF vuông cân tại A . Đặt AF = a và
=α . GọiJ = EF ∩AI . Cho hình vẽ quay quanh đường thẳng AI cố định. Thể tích của hình sinh bởi tam giác AFJ theo a và α. -
Cho hai mặt cầu [S1] tâm O1, bán kính R1và [S2] tâm O2, bán kính R2[R1< R2] tiếp xúc ngoài với nhau tại P. Gọi [S] là mặt cầu đường kính AB màAvà B là giao điểm của mặt cầu [S1] và [S2] với đường thẳng O1O2.Mặt phẳng [α] qua P và vuông góc với O1O2, cắt mặt cầu [S] theo một đường tròn [C].Gọi [P1] là tiếp diện của [S1] tại A và [P2] là mặt phẳng vuông góc tại B với đường thẳng O1O2. Câu nào sau đây đúng?
-
Cho hai mặt cầu [S1] tâm O1, bán kính R1và [S2] tâm O2, bán kính R2[R1< R2] tiếp xúc ngoài với nhau tại P. Gọi [S] là mặt cầu đường kính AB màAvà B là giao điểm của mặt cầu [S1] và [S2] với đường thẳng O1O2.Mặt phẳng [α] qua P và vuông góc với O1O2, cắt mặt cầu [S] theo một đường tròn [C].Tập hợp những điểm M sao cho d[M , [α]] = 2R1 là:
-
Trong mặt phẳng [α], cho đường tròn [C] tâm O, bán kính R và đường thẳng dtiếp xúc với [C ] tại I. Cho hình vẽ quay quanh đường thẳng OI. Gọi [S] là hìnhdo [C] sinh ra ; [P] là hình do d sinh ra.Gọi I' là điểm đối xứng của I qua O. Độ dài của đoạn thẳng II' bằng:
-
Cho đường thẳng Δcố định trên đó có hai điểm A và B phân biệt. Gọi [CM] là đường tròn qua điểm M nhận Δlàm trục của nó.Nếu A và B cố định với AB = 2a [a là độ dài cho sẵn] vàMA2 + MB2 = 3a2 thì tập hợp những đường tròn [CM] là:
-
Cho mặt cầu S[O ; R] và điểm A thuộc [S]; [P] là mặt phẳng qua O, [P] ∩ [S] = [C]. Gọi [C'] là đường tròn đường kính OA nằm trong [P]; Δlà trục của [C'] và Δ' là tiếp tuyến của [S] vuông góc với [P] tại A . Gọi
[T] là mặt trụvà Nlà mặt nón trục Δ', đỉnh A, nửa góc ở đỉnh là45°.Giao tuyến của [S] và [T] là:
Một số câu hỏi khác có thể bạn quan tâm.
-
Question 46:It can be inferred from the passage that John Adams was______________
The White House, the official home of the United States president, was not built in time for George Washington to live in it. It was begun in 1792 and was ready for its first inhabitants. President and Mrs. John Adams, who moved in on November 1, 1800. When the Adamses moved in, the White House was not yet complete, and the Adamses suffered many inconveniences; for example, the main staircase was incomplete, which hindered movement from floor to floor, and the future laundry yard was merely a pool of mud, so wet laundry was hung in the unfinished East Room to dry. Thomas Jefferson, the third president, improved the comfort of the White House in many respects and added new architectural features such as the terraces on the east and west ends. When the British forces burned the White House on August 24, 1814, President Madison was forced to leave. All the remained after the fire was the exterior walls, the interior was completely destroyed. It was not until December of 1817 that the following president, James Monroe, was able to move into a rebuilt residence. Since then, the White House has continued to be modified but has been continuously occupied by each succeeding U.S president.
-
Question 45:The word “inhabitants” in line 2 is closest meaning to _________
The White House, the official home of the United States president, was not built in time for George Washington to live in it. It was begun in 1792 and was ready for its first inhabitants. President and Mrs. John Adams, who moved in on November 1, 1800. When the Adamses moved in, the White House was not yet complete, and the Adamses suffered many inconveniences; for example, the main staircase was incomplete, which hindered movement from floor to floor, and the future laundry yard was merely a pool of mud, so wet laundry was hung in the unfinished East Room to dry. Thomas Jefferson, the third president, improved the comfort of the White House in many respects and added new architectural features such as the terraces on the east and west ends. When the British forces burned the White House on August 24, 1814, President Madison was forced to leave. All the remained after the fire was the exterior walls, the interior was completely destroyed. It was not until December of 1817 that the following president, James Monroe, was able to move into a rebuilt residence. Since then, the White House has continued to be modified but has been continuously occupied by each succeeding U.S president.
-
Question 42:It’s probable that the next paragraph would discuss ________
As viewed from space, Earth’s distinguishing characteristics are its blue waters and white clouds. Enveloped by an ocean of air consisting of 78% nitrogen and 21% oxygen, the planet is the only one in our solar system known to harbor life. Circling the Sun at an average distance of 149 million kilometers [ 93 million miles], Earth is the third planet from the Sun and the fifth largest planet in the solar system. Our planet’s rapid spin and molten nickel-iron core give rise to an extensive magnetic field which, coupled the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth’s atmosphere protects us from meteors as well, most of which burn up in the Earth’s atmosphere before they can strike the surface. The planet active geological processes have left no evidence of the ancient pelting it almost certainly received soon after it formed about 4.6 billion years ago. The Earth has a single natural satellite–the moon.
-
Question41:The word distinguishing as it is used in this selection means ________.
As viewed from space, Earth’s distinguishing characteristics are its blue waters and white clouds. Enveloped by an ocean of air consisting of 78% nitrogen and 21% oxygen, the planet is the only one in our solar system known to harbor life. Circling the Sun at an average distance of 149 million kilometers [ 93 million miles], Earth is the third planet from the Sun and the fifth largest planet in the solar system. Our planet’s rapid spin and molten nickel-iron core give rise to an extensive magnetic field which, coupled the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth’s atmosphere protects us from meteors as well, most of which burn up in the Earth’s atmosphere before they can strike the surface. The planet active geological processes have left no evidence of the ancient pelting it almost certainly received soon after it formed about 4.6 billion years ago. The Earth has a single natural satellite–the moon.
-
Question 44:Why did George Washington not live in the White House?
The White House, the official home of the United States president, was not built in time for George Washington to live in it. It was begun in 1792 and was ready for its first inhabitants. President and Mrs. John Adams, who moved in on November 1, 1800. When the Adamses moved in, the White House was not yet complete, and the Adamses suffered many inconveniences; for example, the main staircase was incomplete, which hindered movement from floor to floor, and the future laundry yard was merely a pool of mud, so wet laundry was hung in the unfinished East Room to dry. Thomas Jefferson, the third president, improved the comfort of the White House in many respects and added new architectural features such as the terraces on the east and west ends. When the British forces burned the White House on August 24, 1814, President Madison was forced to leave. All the remained after the fire was the exterior walls, the interior was completely destroyed. It was not until December of 1817 that the following president, James Monroe, was able to move into a rebuilt residence. Since then, the White House has continued to be modified but has been continuously occupied by each succeeding U.S president.
-
Question 43:Which of the following would be the most appropriate title for this text?
The White House, the official home of the United States president, was not built in time for George Washington to live in it. It was begun in 1792 and was ready for its first inhabitants. President and Mrs. John Adams, who moved in on November 1, 1800. When the Adamses moved in, the White House was not yet complete, and the Adamses suffered many inconveniences; for example, the main staircase was incomplete, which hindered movement from floor to floor, and the future laundry yard was merely a pool of mud, so wet laundry was hung in the unfinished East Room to dry. Thomas Jefferson, the third president, improved the comfort of the White House in many respects and added new architectural features such as the terraces on the east and west ends. When the British forces burned the White House on August 24, 1814, President Madison was forced to leave. All the remained after the fire was the exterior walls, the interior was completely destroyed. It was not until December of 1817 that the following president, James Monroe, was able to move into a rebuilt residence. Since then, the White House has continued to be modified but has been continuously occupied by each succeeding U.S president.
-
Question 38:What two factors help protect the Earth from radiation?
As viewed from space, Earth’s distinguishing characteristics are its blue waters and white clouds. Enveloped by an ocean of air consisting of 78% nitrogen and 21% oxygen, the planet is the only one in our solar system known to harbor life. Circling the Sun at an average distance of 149 million kilometers [ 93 million miles], Earth is the third planet from the Sun and the fifth largest planet in the solar system. Our planet’s rapid spin and molten nickel-iron core give rise to an extensive magnetic field which, coupled the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth’s atmosphere protects us from meteors as well, most of which burn up in the Earth’s atmosphere before they can strike the surface. The planet active geological processes have left no evidence of the ancient pelting it almost certainly received soon after it formed about 4.6 billion years ago. The Earth has a single natural satellite–the moon.
-
Question 37:Which of the following helps to create the Earth’s magnetic fields?
As viewed from space, Earth’s distinguishing characteristics are its blue waters and white clouds. Enveloped by an ocean of air consisting of 78% nitrogen and 21% oxygen, the planet is the only one in our solar system known to harbor life. Circling the Sun at an average distance of 149 million kilometers [ 93 million miles], Earth is the third planet from the Sun and the fifth largest planet in the solar system. Our planet’s rapid spin and molten nickel-iron core give rise to an extensive magnetic field which, coupled the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth’s atmosphere protects us from meteors as well, most of which burn up in the Earth’s atmosphere before they can strike the surface. The planet active geological processes have left no evidence of the ancient pelting it almost certainly received soon after it formed about 4.6 billion years ago. The Earth has a single natural satellite–the moon.
-
Question 40:The main idea of this passage is that ________
As viewed from space, Earth’s distinguishing characteristics are its blue waters and white clouds. Enveloped by an ocean of air consisting of 78% nitrogen and 21% oxygen, the planet is the only one in our solar system known to harbor life. Circling the Sun at an average distance of 149 million kilometers [ 93 million miles], Earth is the third planet from the Sun and the fifth largest planet in the solar system. Our planet’s rapid spin and molten nickel-iron core give rise to an extensive magnetic field which, coupled the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth’s atmosphere protects us from meteors as well, most of which burn up in the Earth’s atmosphere before they can strike the surface. The planet active geological processes have left no evidence of the ancient pelting it almost certainly received soon after it formed about 4.6 billion years ago. The Earth has a single natural satellite–the moon.
-
Question 39:The word consisting most nearly means ________
As viewed from space, Earth’s distinguishing characteristics are its blue waters and white clouds. Enveloped by an ocean of air consisting of 78% nitrogen and 21% oxygen, the planet is the only one in our solar system known to harbor life. Circling the Sun at an average distance of 149 million kilometers [ 93 million miles], Earth is the third planet from the Sun and the fifth largest planet in the solar system. Our planet’s rapid spin and molten nickel-iron core give rise to an extensive magnetic field which, coupled the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth’s atmosphere protects us from meteors as well, most of which burn up in the Earth’s atmosphere before they can strike the surface. The planet active geological processes have left no evidence of the ancient pelting it almost certainly received soon after it formed about 4.6 billion years ago. The Earth has a single natural satellite–the moon.