From a point PP outside a circle with center OO, tangents PAPA and PBPB are drawn to the circle. The line segment formed by joining the points AA and BB intersect the line segment OPOP at MM. Find the measure of AMPAMP.
A O P B M


Answer:

9090

Step by Step Explanation:
  1. Given:
    PAPA and PBPB are the tangents to the circle from an external point PP.

    To find:
    The measure of AMPAMP.
  2. In MAPMAP and MBPMBP, we have [Math Processing Error] Thus, MAPMBP   [By SAS-congruence]
  3. As the corresponding parts of congruent triangles are equal, MA=MB and AMP=BMP.

    Also, [Math Processing Error]
  4. Therefore, the measure of AMP is 90.

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