Prove that the circles described with the four sides of a rhombus, as diameters, pass through the point of intersection of its diagonals.
Let diagonals BD and AC of the rhombus ABCD intersect at O.
We know that the diagonals of a rhombus bisect each other at right angles.
∴ ∠BOC = 90°
∴∠BOC lies in a circle.
The circle drawn with BC as diameter will pass through O.
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