MathDB

Given a triangle

ABC

such that

AB<AC

. On sides

AB

and

BC

, points

P

and

Q

are marked respectively such that the lines

AQ

and

CP

are perpendicular, and the circle inscribed in the triangle

ABC

touches the length

PQ

. The line

CP

intersects the circle circumscribed around the triangle

ABC

at the points

C

and

T

. If the lines

CA,PQ

and

BT

intersect at one point, prove that the angle

\angle CAB

is right.

Problem Statement