Q. 24.3( 310 Votes )

# In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to

A. 60° B. 70°

C. 80° D. 90°

Answer :

Given: TP and TQ are tangents.

Therefore, radius drawn to these tangents from centre of the circle will be perpendicular to the tangents.

Thus, OP ⊥ TP and OQ ⊥ TQ

And therefore,∠OPT = 90°

∠OQT = 90°

In quadrilateral POQT,

Sum of all interior angles = 360°

∠OPT + ∠POQ +∠OQT + ∠PTQ = 360°

90°+ 110° + 90° + ∠PTQ = 360°

**∠PTQ = 70°**

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PREVIOUSFrom a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle isA. 7 cm B. 12 cmC. 15 cm D. 24.5 cmNEXTIf tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal toA. 50° B. 60°C. 70° D. 80°

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