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Question -

Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.



Answer -

Let MN is the diameter and chord AB of circle C(O, r) then according to the question
AP = BP.
Then we have to prove that  .
Join OA and OB.
In ΔAOP and ΔBOP
           (Radii of the same circle)
AP = BP         (P is the mid point of chord AB)
OP = OP         (Common)
Therefore,  
                       (by cpct)
 
Hence, proved.

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