MathDB

AD: DC, interesections of internal and external bisectors of C with circumcircle

Source: Switzerland - Swiss &Mu;&Omicron; 2015 p1

July 15, 2020

angle bisectorratiogeometrycircumcircle

Problem Statement

Let

ABC

be an acute-angled triangle with

AB \ne BC

and radius

k

. Let

P

and

Q

be the points of intersection of

k

with the internal bisector and the external bisector of

\angle CBA

respectively. Let

D

be the intersection of

AC

and

PQ

. Find the ratio

AD: DC