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Tangent circles

Source: St Petersburg Olympiad 2018, Grade 11, P3

June 21, 2018

geometry

Problem Statement

Point

T

lies on the bisector of

\angle B

of acuteangled

\triangle ABC

. Circle

S

with diameter

BT

intersects

AB

and

BC

at points

P

and

Q

. Circle, that goes through point

A

and tangent to

S

at

P

intersects line

AC

at

X

. Circle, that goes through point

C

and tangent to

S

at

Q

intersects line

AC

at

Y

. Prove, that

TX=TY

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