MathDB

Easy circle and tangents

Source: Bosnia and Herzegovina TST 2014 day 1 problem 1

May 10, 2014

trigonometrygeometry unsolvedgeometry

Problem Statement

Let

k

be the circle and

A

and

B

points on circle which are not diametrically opposite. On minor arc

AB

lies point arbitrary point

C

. Let

D

E

and

F

be foots of perpendiculars from

C

on chord

AB

and tangents of circle

k

in points

A

and

B

. Prove that

CD= \sqrt {CE \cdot CF}