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If P, Q, and R are three distinct points, do line segments PQ and PR

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Bunuel
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If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  18 Dec 2014, 06:02
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If P, Q, and R are three distinct points, do line segments PQ and PR have the same length ?

(1) P is the midpoint of line segment QR.
(2) Q and R lie on the same circle with center P.
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  18 Dec 2014, 06:09
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D.
S1- As P is the mid point of QR PQ and PR must be same length.
S2- Q n R lies on the same circle(i.e. is equal distance from center P as both are the radius of the circle).So, PQ=PR.
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  18 Dec 2014, 07:10
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1.no explaination needed i think. Sufficeint

2. All points on a circle lies on equal distance from center. Sufficient

Ans D
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  19 Dec 2014, 10:10
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If P, Q, and R are three distinct points, do line segments PQ and PR have the same length ?

(1) P is the midpoint of line segment QR.
(2) Q and R lie on the same circle with center P.

Solution:
Lengths PQ=PR?

Statement 1: P is the midpoint of line segment QR
Thus PQ=PR - Sufficient

Statement 2: Q and R lie on the same circle with center P
PQ = radius of circle
PR = radius of circle
Thus PQ=PR - Sufficient

Each statement alone is sufficient. Answer D
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Bunuel
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  22 Dec 2014, 06:52
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Bunuel wrote:

Tough and Tricky questions: Geometry.



If P, Q, and R are three distinct points, do line segments PQ and PR have the same length ?

(1) P is the midpoint of line segment QR.
(2) Q and R lie on the same circle with center P.

Kudos for a correct solution.


The correct answer is D.
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  19 May 2016, 12:23
The question is basically asking us whether length (PQ) = length (PR)

Statement 1 tells us point P is midpoint of line segment QR. points lie in the order Q---P---R or R---P---Q
It means that length (PQ) = length (PR) So sufficient

Statement 2 tells us that Q and R are endpoints of arc represented in a circle with center P.
It means that PQ and PR are radius of the circle. we know that radius of a circle are equal in lengths,so length (PQ) = length (PR)
so sufficient

Correct Answer - D
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink] New post  11 Aug 2023, 19:53
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Re: If P, Q, and R are three distinct points, do line segments PQ and PR [#permalink]
11 Aug 2023, 19:53
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