- 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∘, so:
∠OTP=∠OTQ=90∘
- Also, we know that ∠PTQ=∠OTP+∠OTQ, which means:
∠PTQ=90∘+90∘=180∘
- Therefore, ∠PTQ=2∠OPQ.