Q. 115.0( 1 Vote )

# If two chords AB and CD of a circle with centre O, when produced intersect each other at the point P, let us prove that ∠AOC - ∠BOD = 2 ∠BPC.

The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

Similarly, the angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

BOD = 2BCD.

In ΔBPC, ABC = BPC + BCP

On substituting the values of ABC and BCP in above

equation, we get,

AOC - BOD = 2 BPC

Hence, proved.

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