Question

Which of the following statements is true?

Answer 1

Given:

A figure of a circle.

To find:

The correct statement for the given figure.

Solution:

According to the tangent secant theorem, if two tangents or two secants are drawn to the circle from an exterior point, then the measure of angle between the tangents or secants is:

$\text{Exterior angle}=\dfrac{1}{2}(\text{Difference between intercepted arcs})$

$\text{Exterior angle}=\dfrac{1}{2}(\text{Larger arc - smaller arc})$

In the given figure, the exterior angle is 32 degrees, larger arc is QAI and smaller arc is QI.

$32^\circ=\dfrac{1}{2}(m(arcQAI)-m(arcQI))$

Therefore, the correct option is C.