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 = 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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