MathDB

concyclic wanted, diameter of a circle, tangent related

Source: 2019 (-20) Swedish Mathematical Competition p2

August 30, 2020

geometryConcyclicdiametertangent

Problem Statement

Segment

AB

is the diameter of a circle. Points

C

and

D

lie on the circle. The rays

AC

and

AD

intersect the tangent to the circle at point

B

at points

P

and

Q

, respectively. Show that points

C, D, P

and

Q

lie on a circle.