MathDB

Very similar to ELMO 2016/6

Source: Russian TST 2016, Day 12 P3

April 20, 2023

geometryincircle

Problem Statement

The scalene triangle

ABC

has incenter

I{}

and circumcenter

O{}

. The points

B_A

and

C_A

are the projections of the points

B{}

and

C{}

onto the line

L_A

. A circle with a diameter

B_AC_A

intersects the line

BC

at the points

K_A

and

L_A

.
[*]Prove that the circumcircle of the triangle

AK_AL_A

touches the incircle of the triangle

ABC

at some point

T_A

. [*]Define the points

T_B

and

T_C

analogously. Prove that the lines

AT_A,BT_B

and

CT_C

intersect on the line

OI

.

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