neeti2711 wrote: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 the segment QR
(2) Q and R lie on the same circle with center P

Target question: Does PQ = PR ?

Statement 1: P is the midpoint of the segment QR
From the definition of midpoint, this statement tells us that PQ must equal PR
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Q and R lie on the same circle with center P
If P is the center of a circle, then PQ and PR are both radii of that circle.
Since all radii of a circle have the same length, PQ must equal PR
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Good question.

From the Official Guide: A circle is a set of points in a plane that are all located the same distance from a fixed point (the center of the circle).

So, a circle is defined as the points that lie on the circumference.

Later in the OG, we get: A chord of a circle is a line segment that has its endpoints on the circle.

So, if a questions refers to points on a circle, we can read this to mean "on the circumference."

Cheers,
Brent

bnpetteway wrote:@ Brent, Aren't they saying the exact same thing? I got the correct answer as well and just wanted to clarify.

I wouldn't exactly say that they're same thing.

If Q and R lie on the same circle with center P, then we can't necessarily conclude that P is the midpoint of the segment QR.

However, if P is the midpoint of the segment QR then we can conclude that Q and R lie on the same circle with center P

Nevertheless, the answer is still D.

Cheers,
Brent