Question

Cynthia is in the process of constructing two tangent line segments from a point outside circle O to circle O as shown. Which line segments could she draw that would both be tangent to circle O?

A) segments MA and MB
B) segments MB and PB
C) segments PA and MA
D) segments PA and PB

Answer 1

D) segments PA and PB

Explanation:

Answer 2

(B) Segments MA and MB

Explanation:

The tangent to the circle at a point is perpendicular to the radius of the circle drawn to the point of tangency.

Tangent at a point is unique.

Since there can be no two tangents at a point on circle, the options (b) and (c) are ruled out.

Now, if OA is perpendicular to MA, MA is the tangent else if OA is perpendicular to PA, PA is the tangent. Same is the case with point B.

Tangents from the same external point has same length.

MA = MB since they are the radii of the same circle with center M.

Hence, MA and MB meet all the requirements of the tangents.