Question

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

Answer 1

Consider ABCD as a rhombus

We know that the diagonals AC and BD intersect at the point O

From the figure we know that the diagonals of the rhombus bisect at right angles

It can be written as

∠BOC = 90^o

Thus, ∠BOC lies in the circle

We know that the circle can be drawn with BC as the diameter having the centre O

In the same way, all the circles with AB, AD and CD as diameters will pass through the centre O.

Therefore, it is proved that the circles described with the four sides of a rhombus as diameters pass through the point of intersection of its diagonals.