MathDB

Gamma is the second-largest angle

Source: Austrian Federal Competition for Advanced Students 2012, #4

May 23, 2012

geometrycircumcircleincenterangle bisectorperpendicular bisectorgeometry proposed

Problem Statement

Let

ABC

be a scalene (i.e. non-isosceles) triangle. Let

U

be the center of the circumcircle of this triangle and

I

the center of the incircle. Assume that the second point of intersection different from

C

of the angle bisector of

\gamma = \angle ACB

with the circumcircle of

ABC

lies on the perpendicular bisector of

UI

. Show that

\gamma

is the second-largest angle in the triangle

ABC