MathDB

Parallel lines and tangents

Source: Bosnia and Herzegovina TST 2016 day 1 problem 1

May 16, 2016

geometryTangentscircleparallelcollinear

Problem Statement

Let

ABCD

be a quadrilateral inscribed in circle

k

. Lines

AB

and

CD

intersect at point

E

such that

AB=BE

. Let

F

be the intersection point of tangents on circle

k

in points

B

and

D

, respectively. If the lines

AB

and

DF

are parallel, prove that

A

C

and

F

are collinear.