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