MathDB

Given a circle with diameter

AB

and a point

X

on the circle different from

A

and

B

, let

t_{a}

t_{b}

and

t_{x}

be the tangents to the circle at

A

B

and

X

respectively. Let

Z

be the point where line

AX

meets

t_{b}

and

Y

the point where line

BX

meets

t_{a}

. Show that the three lines

YZ

t_{x}

and

AB

are either concurrent (i.e., all pass through the same point) or parallel. 6762

Problem Statement