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Prove that the circle drawn with any sid...

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

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Let the diagonals AC and BD of a rhombus ABCD intersect at O. But, the diagonals of a rhombus bisect each other at right angles, So, `/_ BOC = 90^(@)`
`:. /_ BOC ` lies in a semicircles.
Thus, the circle drawn with BC as diameter will pass through O. Similarly , all the circles described with AB, AD and CD as diameters , will pass through O.
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