MathDB

Perpendicularity with incenter in a right triangle

Source: RMO Mumbai 2016, P1

October 11, 2016

geometryincenter

Problem Statement

Let

ABC

be a right-angled triangle with

\angle B=90^{\circ}

. Let

I

be the incenter of

ABC

. Draw a line perpendicular to

AI

I

. Let it intersect the line

CB

D

. Prove that

CI

is perpendicular to

AD

and prove that

ID=\sqrt{b(b-a)}

where

BC=a

and

CA=b