AP and BP are the two tangents at the extremities of chord AB of a circle. Prove that ∠MAP is equal to ∠MBP.
Answer:
- Given:
AB is a chord of the circle with center O.
Tangents at the extremities of the chord AB meet at an external point P.
Chord AB intersects the line segment OP at M. - Now, we have to find the measure of ∠MAP.
In △MAP and △MBP, we have - We know that corresponding parts of congruent triangles are equal.
Thus, .