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Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.
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Let ABCD be a rhombus whose diagonals AC and BD intersect at O. We know that, diagonals of a rhombus intersect each other at right angle. Thus, the circles described on the four sides of a rhombus as their respective diameters, pass through the point of intersection of its diagonals. Hence, proved.
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ABCD be a rhombus AC and BD intersect at O.
We know that diagonals of a rhombus intersect each other at right angle.
∠AOB = ∠BOC = ∠COD = ∠AOD = 90°
Circles with AB, BC ,CD and DA as their respective diameters pass through O.
Circles described on the four sides of Enormous as their respective diameters pass to the point of intersection of its diagonals.
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