Advertisements
Advertisements
प्रश्न
Two tangents TP and TQ are drawn from an external point T to a circle with centre O as shown in figure. If they are inclined to each other at an angle of 100°, then what is the value of ∠POQ?
बेरीज
Advertisements
उत्तर
Use the tangent theorem: angle PTQ = 2·angle OPQ.
Given PTQ = 100°, so OPQ = `100^circ/2` = 50°.
In isosceles triangle OPQ (OP = OQ), the base angles are each `(180^circ - ∠POQ)/2` and OPQ is one of these base angles.
Thus `(180^circ - ∠POQ)/2 = 50^circ`
⇒ 180° – ∠POQ = 100°
⇒ ∠POQ = 80°
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
