MathDB

Tangents intersect on AC

Source: All Russian 2017,grade 10,day 2,P8

May 1, 2017

geometrycircumcircleincircleincenterCircumcentergeometric transformationreflection

Problem Statement

In a non-isosceles triangle

ABC

O

and

I

are circumcenter and incenter,respectively.

B^\prime

is reflection of

B

with respect to

OI

and lies inside the angle

ABI

.Prove that the tangents to circumcirle of

\triangle BB^\prime I

B^\prime

I

intersect on

AC

. (A. Kuznetsov)