OA is the radius of a circle with centre at Q, AQ is its chrod and C is any point on the circle. A circle passes through the point O,A,C intesect the chrod AQ at the point P. Prove that CP=PQ

Explanation

OA is the radius of the circle with centre at O and, AQ is its chrod and C is any point on the circle. A circle passes through the point O,A,C intesect the chrod AQ at the poin P. Let us join C,P
To prove : We have to prove that `CP=PQ`
Construction : Let us join `O,C,O,Q and O,P`
Proof : In the circle `APOc, angle OCP` are two angles in circle produced by the chord OP,
`:. angle OAP= angle OCP......(1)`
Again, `DeltaOAQ, OA= OQ[ radii` of the same circle.]
`:. OAQ= angle OQA ,........(2)`
`:.` from (1) and (2) we get, `angle OCP= angle OQA ......(3)`
`:. CP= PQ [ :. "in" Delta CPQ, angle QCP= angle CQP]`
Hene `CP=PQ`