Question

Prove that the circle drawn with any side of a rhombus as diameter

Answer 1

GIVEN ;-

⇒ In the given figure , the following things should be noted -


                                        ⇒ ABCD is a rhombus

                                        ⇒ Diagonals of the rhombus are AC and BD
                                           which intersect at O.

TO PROVE ;-

⇒ ''The circle drawn with any side of a rhombus as diameter''


PROOF ;-

⇒ ∠ AOB = ∠ BOC = ∠ COD = ∠ AOD = 90 [ Diagonal of the rhombus bisect                                                                      each other at  90°]


Now in the given four circles , we have four diameters -  AB , BC , CD , DA.

⇒ All this diameters passes through O. { Angles in a semi circle is right                                                                     angle }
                                                   
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⇒ Therefore by the above information , we proved that the circles described in the four sides of a rhombus as a diameter, pass through the point of intersection of its diagonal.