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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

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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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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Hello from the GMAT Club BumpBot!

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