Let ABC be an equilateral triangle with circumcircle k. A circle q touches k from outside in a point D, where the point D on 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. geometrygeometry proposedtangenttangent linestouching circles