MathDB

CD bisects SQ, 2 circles related

Source: Mathematics Regional Olympiad of Mexico West 2017 P2

September 8, 2022

geometrybisects segment

Problem Statement

From a point

P

, two tangent lines are drawn to a circle

\Gamma

, which touch it at points

A

and

B

. A circle

\Phi

is drawn with center at

P

and passes through

A

and

B

and is taken a point

R

that is on the circumference

\Phi

and in the interior of

\Gamma

. The straight line

PR

intersects

\Gamma

at the points

S

and

Q

. The straight lines

AR

and

BR

meet

\Gamma

again at points

C

and

D

, respectively. Prove that

CD

passes through the midpoint of

SQ

.

Back to Problems View on AoPS