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Question

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

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Solution


Given: A rhombus ABCD and a circle with diameter AB.To prove: Point O lies on the circleProof:As, angle formed in the semi-circle is a right angle.AOB=90°Also, diagonals intersect each other at a right angle.AOB=BOC=COD=DOA=90°So, it can be conlcuded that point O lies on the circle.

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

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