From any point on the circle x^2 + y^2 = a^2, | vedclass

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Question

(C) Let $P$ be any point on the circle $x^2 + y^2 = a^2$. Let $PQ$ and $PR$ be the tangents drawn from $P$ to the circle $x^2 + y^2 = a^2 \sin^2 \alph

Vedclass · Accepted Answer

$2\alpha$

Vedclass · Answer

(C) Let $P$ be any point on the circle $x^2 + y^2 = a^2$. Let $PQ$ and $PR$ be the tangents drawn from $P$ to the circle $x^2 + y^2 = a^2 \sin^2 \alpha$,where $Q$ and $R$ are the points of contact.Let $O$ be the origin $(0, 0)$. The radius of the inner circle is $OQ = a \sin \alpha$.The distance $OP$ is the radius of the outer circle,so $OP = a$.In the right-angled triangle $	riangle OQP$,$\sin(\angle OPQ) = \frac{OQ}{OP} = \frac{a \sin \alpha}{a} = \sin \alpha$.Therefore,$\angle OPQ = \alpha$.The angle between the tangents is $\angle QPR = 2 	imes \angle OPQ = 2\alpha$.

From any point on the circle $x^2 + y^2 = a^2$,tangents are drawn to the circle $x^2 + y^2 = a^2 \sin^2 \alpha$. The angle between them is:

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