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