From any point on the circle {x^2} + {y^2} = | vedclass

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Question

(c) Let any point on the circle

${x^2} + {y^2} = {a^2}$ be $(a\cos t,\,\,a\sin t)$ and $\angle \,OPQ = 	heta $

Now; $PQ = $ length of tangent f

Vedclass · Accepted Answer

$2\alpha $

Vedclass · Answer

(c) Let any point on the circle

${x^2} + {y^2} = {a^2}$ be $(a\cos t,\,\,a\sin t)$ and $\angle \,OPQ = 	heta $

Now; $PQ = $ length of tangent from $P$ on the circle ${x^2} + {y^2} = {a^2}{\sin ^2}\alpha $

$	herefore $ $PQ = $$\sqrt {{a^2}{{\cos }^2}t + {a^2}{{\sin }^2}t - {a^2}{{\sin }^2}\alpha } $$ = a\cos \alpha $

$OQ = $ Radius of the circle

${x^2} + {y^2} = {a^2}{\sin ^2}\alpha $

$OQ = $ $a\sin \alpha $,

$	herefore $$	an 	heta = \frac{{OQ}}{{PQ}} = 	an \alpha $

$\Rightarrow \,	heta = \alpha $

$	herefore $ Angle between tangents $ = \,\angle \,QPR = 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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