MathDB

ratio of segments wanted, incircle, circumcircle, arc midpoint related

Source: 2012 Argentina OMA L3 p3

June 17, 2020

ratiogeometrycircumcirclearc midpointincircle

Problem Statement

In the triangle

ABC

the incircle is tangent to the sides

AB

and

AC

D

and

E

respectively. The line

DE

intersects the circumcircle at

P

and

Q

, with

P

in the small arc

AB

and

Q

in the small arc

AC

. If

P

is the midpoint of the arc

AB

, find the angle A and the ratio

\frac{PQ}{BC}