MathDB

Geometry

Source: Serbia JBMO TST 2020 P1

September 5, 2020

geometry

Problem Statement

Given is triangle

ABC

with arbitrary point

D

on

AB

and central of inscribed circle

I

. The perpendicular bisector of

AB

intersects

AI

and

BI

at

P

and

Q

, respectively. The circle

(ADP)

intersects

CA

at

E

, and the circle

(BDQ)

intersects

BC

at

F

and

(ADP)

intersects

(BDQ)

at

K

. Prove that

E, F, K, I

lie on one circle.

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