MathDB

A, B, and Q lie on a circle with center T

Source: Finland 2017, p5

September 8, 2019

circleCircumcenterdiametergeometry

Problem Statement

Let

A

and

B

be two arbitrary points on the circumference of the circle such that

AB

is not the diameter of the circle. The tangents to the circle drawn at points

A

and

B

meet at

T

. Next, choose the diameter

XY

so that the segments

AX

and

BY

intersect. Let this be the intersection of

Q

. Prove that the points

A, B

, and

Q

lie on a circle with center

T