AP and BP are the two tangents at the extremities of chord AB of a circle. Prove that MAP is equal to MBP.
A O P B M


Answer:


Step by Step Explanation:
  1. 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.
  2. Now, we have to find the measure of MAP.

    In MAP and MBP, we have PA=PB[Tangents from an external point on a circle are equal in length]  MP=MP[Common]MPA=MPB [Tangents from an external point are equally inclined to   the line segment joining the point to the center.] MAPMBP [by SAS Congruency Criterion] 
  3. We know that corresponding parts of congruent triangles are equal.
    Thus, MAP=MBP.

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