Question 6
If angle between two tangents drawn from a point P to a circle of radius a and centre O is $60^{\circ}$ , then OP = a $\sqrt{3}$ .

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Solution

False

From point P, two tangents PT and PR are drawn.
Given:Radius = a
Also, line OP bisects the $∠$ RPT
$∴ ∠ T P O = ∠ R P O = 30^{\circ}$
Also, $O T ⊥ P T$
$I n r i g h t a n g l e d Δ O T P .$
$S i n 30^{\circ} = \frac{O T}{O P}$
$\Rightarrow \frac{1}{2} = \frac{a}{O P}$
$\Rightarrow O P = 2 a$

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Q. Question 6
If angle between two tangents drawn from a point P to a circle of radius a and centre O is

60^{\circ}

, then OP = a

\sqrt{3}

Q. If the angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP = _______.

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 $O P$ .

State true or false

If angle between two tangents drawn from a point P to a circle of radius a and centre O is

60^{0}

, then OP =

a \sqrt{3}

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Question 6 If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60∘ , then OP = a √3.

False From point P, two tangents PT and PR are drawn. Given:Radius = a Also, line OP bisects the ∠ RPT ∴∠TPO=∠RPO=30∘ Also, OT⊥PTIn right angled ΔOTP.Sin30∘=OTOP ⇒12=aOP ⇒OP=2a

Question 6
If angle between two tangents drawn from a point P to a circle of radius a and centre O is $60^{\circ}$ , then OP = a $\sqrt{3}$ .