Tangents to a circle at points P and Q on the | vedclass

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Question

(c)

Given,

$P R$ and $Q R$ are tangents.

$P Q=6$

$P R=5$

$P M=\frac{1}{2} P Q$

$P M=\frac{1}{2} 	imes 6=3$

In $	riangle P R M$,

Vedclass · Accepted Answer

$\frac{15}{4}$

Vedclass · Answer

(c)

Given,

$P R$ and $Q R$ are tangents.

$P Q=6$

$P R=5$

$P M=\frac{1}{2} P Q$

$P M=\frac{1}{2} 	imes 6=3$

In $	riangle P R M$,

$R M^2 =P R^2-P M^2=25-9=16$

$R M =4$

In $	riangle P R M, \quad 	an 	heta=\frac{P M}{R M}=\frac{3}{4}$

In $	riangle P O R, \quad 	an 	heta=\frac{O P}{P R}=\frac{r}{5}$

From Eqs.$(i)$ and $(ii)$, we get

$\frac{3}{4}=\frac{r}{5} \Rightarrow r=\frac{15}{4}$

Tangents to a circle at points $P$ and $Q$ on the circle intersect at a point $R$. If $P Q=6$ and $P R=5$, then the radius of the circle is

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