Question

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

Answer 1

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° 

Now, 

∠AOB = 90° = 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.