If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then $∠$ TOP is ____.

30^{0}

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60^{0}

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120^{0}

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90^{0}

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Solution

The correct option is B $60^{0}$
Given, OP=2r

Let $∠ T O P = θ$

In $Δ O T P, c o s θ = \frac{O T}{O P} = \frac{r}{2 r} = \frac{1}{2}$

$∵ c o s 60^{0} = \frac{1}{2}$

$∴ θ = 60^{\circ}$

$∴ ∠ T O P = 60^{0}$

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Similar questions

Q. Two tangents PT and PT' are drawn to a circle, with centre O, from an external point P. Prove that

∠

TPT'

= 2 ∠

OTT'.

If the angle between two tangents drawn from an external point $P$ to a circle of radius $a$ and centre $O$ , is $60^{o}$ , then find the length of $O P$ .

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If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then ∠TOP is ____.

The correct option is B 600Given, OP=2r Let ∠TOP=θ In ΔOTP, cos θ=OTOP =r2r =12 ∵cos 600=12 ∴θ=60∘ ∴∠TOP=600

If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then $∠$ TOP is ____.

The correct option is B $60^{0}$
Given, OP=2r

Let $∠ T O P = θ$

In $Δ O T P, c o s θ = \frac{O T}{O P} = \frac{r}{2 r} = \frac{1}{2}$

$∵ c o s 60^{0} = \frac{1}{2}$

$∴ θ = 60^{\circ}$

$∴ ∠ T O P = 60^{0}$