MathDB

Easy Geometry

Source: Iran TST 2015, exam 1, day 1 problem 2

May 10, 2015

geometry

Problem Statement

I_b

is the

B

-excenter of the triangle

ABC

and

\omega

is the circumcircle of this triangle.

M

is the middle of arc

BC

of

\omega

which doesn't contain

A

.

MI_b

meets

\omega

at

T\not =M

. Prove that

TB\cdot TC=TI_b^2.

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