MathDB

BdMO National 2016 Higher Secondary Problem 6

\triangle ABC

is an isosceles triangle with

AC = BC

and

\angle ACB < 60^{\circ}

I

and

O

are the incenter and circumcenter of

\triangle ABC

. The circumcircle of

\triangle BIO

intersects

BC

D \neq B

.
(a) Do the lines

AC

and

DI

intersect? Give a proof.
(b) What is the angle of intersection between the lines

OD

and

IB

6