MathDB

Geometry

Source: RMO 2016 Karnataka Region P5

October 16, 2016

geometry

Problem Statement

Let

ABC

be a right-angled triangle with

\angle B=90^{\circ}

. Let

I

be the incentre if

ABC

. Extend

AI

and

CI

; let them intersect

BC

in

D

and

AB

in

E

respectively. Draw a line perpendicular to

AI

at

I

to meet

AC

in

J

, draw a line perpendicular to

CI

at

I

to meet

AC

at

K

. Suppose

DJ=EK

. Prove that

BA=BC

.

Back to Problems View on AoPS