APAP and BPBP are the two tangents at the extremities of chord ABAB of a circle. Prove that ∠MAP∠MAP is equal to ∠MBP∠MBP.
Answer:
- Given:
ABAB is a chord of the circle with center OO.
Tangents at the extremities of the chord ABAB meet at an external point PP.
Chord ABAB intersects the line segment OPOP at MM. - Now, we have to find the measure of ∠MAP.∠MAP.
In △MAP△MAP and △MBP,△MBP, we have [Math Processing Error] - We know that corresponding parts of congruent triangles are equal.
Thus, ∠MAP=∠MBP.