MathDB

Let

ABC

be an equilateral triangle with circumcircle

k

. A circle

q

touches

k

from outside in a point

D

, where the point

D

k

is chosen so that

D

and

C

lie on different sides of the line

AB

. We now draw tangent lines from

A,B

and

C

to the circle

q

and denote the lengths of the respective tangent line segments by

a,b

and

c

.
Prove that

a+b=c

Problem Statement