Question

In the given figure, two tangents PT and QT are drawn to a circle with centre O from an external point T. Prove that $\angle$ PQT = $2\angle$** OPQ.**

Answer 1

- Let $PT$ and $QT$ be two tangents drawn from the external point $T$ to the circle with center $O$.

- Since $PT$ and $QT$ are tangents, the angle between a tangent and the radius is always $90^\circ$, so:

$\angle OTP = \angle OTQ = 90^\circ$

- Also, we know that $\angle PTQ = \angle OTP + \angle OTQ$, which means:

$\angle PTQ = 90^\circ + 90^\circ = 180^\circ$

- Therefore, $\angle PTQ = 2 \angle OPQ$.