MathDB

comp. geo with circumcircle and another circle

Source: IV Soros Olympiad 1997-98 R3 10.9 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 2, 2024

geometrycircumcircle

Problem Statement

In triangle

ABC

, side

BC

is equal to

a

, and the angles of the triangle adjacent to it are equal to

\alpha

and

\beta

. A circle passing through points

A

and

B

intersects lines

CA

and

CB

for second time at points

P

and

M

. It is known that straight line

RM

passes through the center of the circle circumscribed around

ABC

. Find the length of the segment

PM