MathDB

In an isosceles triangle

ABC

in which

AC = BC

and

\angle ABC < 60^o

I

and

O

are the centers of the inscribed and circumscribed circles, respectively. For the triangle

BIO

, the circumscribed circle intersects the side

BC

again at

D

. Prove that: i) lines

AC

and

DI

are parallel, ii) lines

OD

and

IB

are perpendicular.

Problem Statement