MathDB

We are given a non-isosceles triangle

ABC

with incenter

I

. Show that the circumcircle

k

of the triangle

AIB

does not touch the lines

CA

and

CB

. Let

P

be the second point of intersection of

k

with

CA

and let

Q

be the second point of intersection of

k

with

CB

. Show that the four points

A

B

P

and

Q

(not necessarily in this order) are the vertices of a trapezoid.

Problem Statement