Question

PQ is a chord of length 6cm of a circle of radius 6cm. TP and TQ are tangents of circle at point P and Q. find
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Answer 1

PQ = 6cm

OP = OQ = 6cm

PQ = OP = OQ = 6cm

All sides are equal. Hence, it is an equilateral triangle.

We know that each angle of an equilateral triangle is equal to 60⁰

∠POQ = 60⁰

∠P = ∠Q = 90⁰

(Radius ⊥tangents)

∠T + 90⁰ + 90⁰ + 60⁰ = 360⁰

(Angle sum property of a triangle)

∠T = 360 - 240

∠T = 120⁰

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Answer 2

Given:-

• PQ = 6cm
• OP = OQ = 6cm

In △OPQ,

• PQ = 6cm
• OP = OQ = 6cm

All sides are eequal hence, △OPQ is an equilateral triangle.

∠OPQ = ∠QOP = ∠POQ = 60°

(In an equilateral triangle all angles are equal to 60°)

∠POQ + ∠PTQ = 180°

(The angles between two tangents drawn from an external point to a circle is supplementary to the angle subtended bye the line Segment joining the points of contact at the center)

60° + ∠PTQ = 180°

∠PTQ = (180 - 60)°

∠PTQ = 120°

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