MathDB

2003 KJMO P3

Source: 2003 Korea Junior Math Olympiad

June 29, 2024

geometryratiocircle

Problem Statement

Consider a triangle

ABC

, inscribed in

O

and

\angle A < \angle B

. Some point

P

outside the circle satisfies

\angle A=\angle PBA =180^{\circ}- \angle PCB

Let

CQ : AB=AQ^2:AD^2

be the intersection of line

PB

and

O

(different from

B

), and

Q

the intersection of the tangent line of

O

passing through

A

and line

CD

. Show that

CQ : AB=AQ^2:AD^2

.

Back to Problems View on AoPS