Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

Question

Philoid · Accepted Answer

Let ABCD be a rhombus in which diagonals intersect at point O and a circle is drawn is drawn taking side CD as diameter

Now,

∠COD = 90⁰

(Since, diagonals of rhombus intersect at 90⁰)

Hence,

∠AOB = ∠BOC = ∠COD = ∠DOA = 90⁰

Hence, point O has to lie on the circle