MathDB

<TSC=<BAC wanted, parallelogram, circumcircle (2020 Kyiv City MO Round2 11.2)

Source:

September 21, 2020

geometryparallelogramcircumcircleequal angles

Problem Statement

A point

P

was chosen on the smaller arc

BC

of the circumcircle of the acute-angled triangle

ABC

. Points

R

and

S

on the sides

AB

and

AC

are respectively selected so that

CPRS

is a parallelogram. Point

T

on the arc

AC

of the circumscribed circle of

\vartriangle ABC

such that

BT \parallel CP

. Prove that

\angle TSC = \angle BAC

.
(Anton Trygub)