From a point P outside a circle with center O, tangents PA and PB are drawn to the circle. The line segment formed by joining the points A and B intersect the line segment OP at M. Find the measure of ∠AMP.
Answer:
90∘
- Given:
PA and PB are the tangents to the circle from an external point P.
To find:
The measure of ∠AMP. - In △MAP and △MBP, we have Thus,
- As the corresponding parts of congruent triangles are equal, and
Also, - Therefore, the measure of is .