Multiple choice

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Then ∠PTQ equals to - O केंद्र वाले वृत्त पर एक बाह्य बिंदु T से दो स्पर्श रेखा TP और TQ खींची जाती है, तो ∠PTQ बराबर है -

  1. ∠OPQ

  2. 2∠ OPQ

  3. 1/2 ∠ OPQ

  4. 1/3∠ OPQ

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since TP and TQ are tangents from point T, they are equal in length and OT bisects ∠PTQ. In right triangle OPQ, ∠OPQ is the angle between OP and PQ. The angle ∠PTQ is external to triangle OPQ and equals 2∠OPQ. This is a standard property: the angle between two tangents equals the difference in the arcs they intercept, which is twice the angle in the alternate segment.