Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.

Question

Philoid · Accepted Answer

Let ABCD be a rhombus such that its diagonals AC and BD intersects at O

Since, the diagonals of a rhombus intersect at right angle

Therefore,

∠ACB = ∠BOC = ∠COD = ∠DOA = 90^o

Now,

∠AOB = 90^o = circle described on AB as diameter will pass through O

Similarly, all the circles described on BC, AD and CD as diameter pass through O.