MathDB

Incenter inside the incircle

Source: Iran 2nd round 2012-Day2-P6

May 1, 2012

geometryincentergeometric transformationreflectioncircumcircleangle bisectorcongruent triangles

Problem Statement

The incircle of triangle

ABC

, is tangent to sides

BC,CA

and

AB

D,E

and

F

respectively. The reflection of

F

with respect to

B

and the reflection of

E

with respect to

C

are

T

and

S

respectively. Prove that the incenter of triangle

AST

is inside or on the incircle of triangle

ABC

.
Proposed by Mehdi E'tesami Fard