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 22\angle OPQ.
Problem Figure

Updated On: Dec 14, 2024
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Solution and Explanation

- Let PTPT and QTQT be two tangents drawn from the external point TT to the circle with center OO.

- Since PTPT and QTQT are tangents, the angle between a tangent and the radius is always 9090^\circ, so:

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

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

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

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

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