According to the equation Lets suppose that X and Y are two circle touch each other at P AB is the common tangent to circle X and Y at point A and B. According in the given figure, In triangle PAC , ∠CAP = ∠APC = α similarly CB = CP , ∠CPB = ∠PBC = β Now triangle APB, ∠PAB + ∠PBA + ∠APB = 180 α + β + (α + β) = 180 2α + 2β = 180 α + β = 90 ∴ ∠APB = 90 = α + β This is the required solution