MathDB

point B in segment AC, 3 circles of diameter AB,BC,AC

Source: Rioplatense Olympiad 2014 level 3 P5

September 4, 2018

geometrycirclesdiameter

Problem Statement

In the segment

A C

a point

B

is taken. Construct circles

T_1, T_2

and

T_3

of diameters

A B, BC

and

AC

respectively. A line that passes through

B

cuts

T_3

in the points

P

and

Q

, and the circles

T_1

and

T_2

respectively at points

R

and

S

. Prove that

PR = Q S