Question

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

Answer 1

We know that the diagonals of a rhombus bisect each other at right angles. 

∴  ∠ APO =90°  - (1) 

Also, AD is the diameter of the circle with centre 0 

∴ ∠ APD=90° - (2)    (Angle in semi circle) 

From ( 1) and (2), we get, The cirde drawn with any side of a rhombus as a diameter, passes through point of intersection of its diagonals.