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 ∠AMP∠AMP.
Answer:
90∘90∘
- Given:
PAPA and PBPB are the tangents to the circle from an external point PP.
To find:
The measure of ∠AMP∠AMP. - In △MAP△MAP and △MBP△MBP, we have [Math Processing Error] Thus, △MAP≅△MBP [By SAS-congruence]
- As the corresponding parts of congruent triangles are equal, MA=MB and ∠AMP=∠BMP.
Also, [Math Processing Error] - Therefore, the measure of ∠AMP is 90∘.