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.
Answer :
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 = 2∠BCD.
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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