Question

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

Answer 1

Data: ABCD is a rhombus. Circle is drawn taking side CD diameter. 

Let the diagonals AC and BD intersect at ‘O’. 

To Prove: Circle passes through the point ‘O’ of intersection of its diagonals. 

Proof: ∠DOC = 90° (Angle in the semicircle) and diagonals of rhombus bisect at right angles at ‘O’. 

∴ ∠DOC = ∠COB = ∠BOA = ∠AOD = 90° 

∴ Circle passes the point of intersection of its diagonal through ‘O’.