Question

MN is a tangent to the circle at the point of contact C. Identify the angle that is equal to x.

• A.
• B.
• C.

Answer 1

The correct option is A

We need to find the angle that is in alternate segment to x.

x is the angle between the tangent MN and the chord BC.
We know that, the angle between a tangent of a circle and a chord drawn from the point of contact is congruent to the angle inscribed in the arc opposite to the arc intercepted by that angle.
We look at the chord BC and find that it subtends angle CAB in the opposite segment.
So, $\angle CAB$ is equal to x.