In the given figure, two circles intersect at A, B and AC, AD are respectively the diameters of the circles. Prove that the points C, B and D are collinear

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Given Two circles with AC and AD as diameters respectively intersecting each other at A and B.

To prove Points C, B and D are collinear. Construction Join CB, BD and AB.

We know that the angle in a semi-circle is 90°.

∠ABC = 90° and ∠ABD = 90°

[∴ AC and AD are diameters of circles]

Then, ∠ABC + ∠ABD = 90° + 90° = 180°

∴CBD is a straight line.

Hence, points C, B and D are collinear.