From a point PPP outside a circle with center OOO, tangents PAPAPA and PBPBPB are drawn to the circle. The line segment formed by joining the points AAA and BBB intersect the line segment OPOPOP at MMM. Find the measure of AMPAMPAMP.
A O P B M


Answer:

909090

Step by Step Explanation:
  1. Given:
    PAPAPA and PBPBPB are the tangents to the circle from an external point PPP.

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

    Also, [Math Processing Error]
  4. Therefore, the measure of AMPAMP is 9090.

You can reuse this answer
Creative Commons License