Question

25. Two circles with centres O and P intersect at A and D, as shown in the figure. If AOB and APC are diameters, prove that B, D and Care collinear.​

Answer 1

Step-by-step explanation:

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Answer 2

Join CB, BD and AB, Since, AC is a diameter of the circle with centre O.

∴ ∠ABC = 90° [angle in semi circle] ---- (i)

Also, AD is a diameter of the circle with center O .

∴ ∠ABD = 90° [angle in semi circle] ---- (ii)

on adding Eqns, (i) and (ii) we get

⇒ ∠ABC + ∠ABD = 180°

So. CBD is a straight line.

Hence C, B and D are collinear .

Hence proved.

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