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Three different points A, B, and C are equidistant from point O. Which
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21 Jun 2023, 03:24
21 Jun 2023, 03:24
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Three different points A, B, and C are equidistant from point O. Which of the following could be true for the given three points?
Indicate all that apply
1) A, B, C, and O all four points lie in the same plane.
2) A, B, and C points lie in the same plane.
3) A, B, and C lie on a straight line.
4) A, B, and C lie on a sphere with O as origin.
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Indicate all that apply
1) A, B, C, and O all four points lie in the same plane.
2) A, B, and C points lie in the same plane.
3) A, B, and C lie on a straight line.
4) A, B, and C lie on a sphere with O as origin.
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
Re: Three different points A, B, and C are equidistant from point O. Which
[#permalink]
25 Jul 2023, 10:07
25 Jul 2023, 10:07
Expert Reply
OE
Three different points A, B and C are equidistant from point O.
A) All four points can be in the same plane.
Consider a circle having center as O and A, B and C lie on the circumference. Hence,
Answer choice A is the Answer.
B) A, B and C points lie on the same plane.
Assume a cone where the vertex of the cone is O and A, B and C lie on the
circumference of the cone. So, this is also possible. Hence, Answer choice B is the
Answer.
C) A, B and C lie on a straight line.
As there is no point which is equidistant for three different points on a straight line,
hence Answer choice C is not the Answer.
D) A, B and C lie on a sphere with O as origin.
For a sphere, every point on the surface of the sphere is equidistant from the origin of
the sphere.
Hence, Answer choice D is the Answer.
Ans. (A, B, D)
Three different points A, B and C are equidistant from point O.
A) All four points can be in the same plane.
Consider a circle having center as O and A, B and C lie on the circumference. Hence,
Answer choice A is the Answer.
B) A, B and C points lie on the same plane.
Assume a cone where the vertex of the cone is O and A, B and C lie on the
circumference of the cone. So, this is also possible. Hence, Answer choice B is the
Answer.
C) A, B and C lie on a straight line.
As there is no point which is equidistant for three different points on a straight line,
hence Answer choice C is not the Answer.
D) A, B and C lie on a sphere with O as origin.
For a sphere, every point on the surface of the sphere is equidistant from the origin of
the sphere.
Hence, Answer choice D is the Answer.
Ans. (A, B, D)
gmatclubot
Re: Three different points A, B, and C are equidistant from point O. Which [#permalink]
25 Jul 2023, 10:07
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