Now extend the segments DB and DA to DE and DF respectively.

Lable the point G where DE intersects the circle K.

Given the point A and the straight line BC.

 

 

Construct an equilateral triangle on the line AB. (Prop1-1)

Construct a circle with center B and radius BC.

 

Next, construct a circle of radius DG with center D.

Note that BC and BG are the same length.

The length of DG is the same as the length of BC plus DB, and the length of DH is the same as the length AH plus AD.

Since DG and DH are radii of the circle K, they are equal. Also DB and DA are equal.

Thus AH and BC are equal.

QED