Question

What property would you use to find angle PTQ?

• A. Lengths of tangents drawn from an external point are equal.
• B. The tangents and the chord between the points of contact form an isosceles triangle.
• C. Radius is perpendicular to the tangent at the point of contact.
• D. There can be only two tangents to the circle from point T.

Answer 1

The correct option is C Radius is perpendicular to the tangent at the point of contact.

In the figure above, we know the $\angle POQ$
We need to find $\angle PTQ.$
For that, first, we need the values of $\angle OPT$ and $\angle OQT$

Now we know a theorem that gives us the angle between a tangent and a radius at the point of contact.

We know that PT and QT are tangents to the circle, and OP and OQ are the radii.

Thus, $\angle OPT$ and $\angle OQT$ are angles between tangents and their corresponding radii.

Hence, we must use the theorem that states that a tangent is perpendicular to the radius at the point of contact.