APAP and BPBP are the two tangents at the extremities of chord ABAB of a circle. Prove that MAPMAP is equal to MBPMBP.
A O P B M


Answer:


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

    In MAPMAP and MBP,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.

You can reuse this answer
Creative Commons License