Suppose S₁ and S₂ are two unequal circles, A B and C D are direct common tangents to these circl

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10-1.Circle and System of Circles

normal

Suppose $S_1$ and $S_2$ are two unequal circles, $A B$ and $C D$ are the direct common tangents to these circles. A transverse common tangent $P Q$ cuts $A B$ in $R$ and $C D$ in $S$. If $A B=10$, then $R S$ is

$8$

$9$

$10$

$11$

(KVPY-2014)

Solution

(c)

Given,

$A B$ and $C D$ are direct common tangents on circle $P Q$ is transverse common tangent $P Q$ cuts $A B$ in $R$ and $C D$ in $S$.

$A B=10$

$R P=R A$

$[\because$ tangents from external point on a circle are equal]

Similarly

$R Q=R B$

$S P=S C$

$R S=S P+P Q+R Q$

$R S=S P+R P$

$R S=S P+R A$

$R S=S P+A B-R B \quad \ldots( i )$

$S Q=S D$

$R S-Q R =C D-C S$

$R S =Q R+C D-C S$

$R S =R B+A B-S P \ldots \text { (ii) }$

From Eqs.$(i)$ and $(ii)$, we get

$S P=R B$

$R S=S P+A B-R B$

$R S=A B=10$

Standard 11

Mathematics

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medium

Suppose $S_1$ and $S_2$ are two unequal circles, $A B$ and $C D$ are the direct common tangents to these circles. A transverse common tangent $P Q$ cuts $A B$ in $R$ and $C D$ in $S$. If $A B=10$, then $R S$ is

Solution

Similar Questions

Choose the incorrect statement about the two circles whose equations are given below $x^{2}+y^{2}-10 x-10 y+41=0$ and $x^{2}+y^{2}-16 x-10 y+80=0$

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Choose the incorrect statement about the two circles whose equations are given below

$x^{2}+y^{2}-10 x-10 y+41=0$ and $x^{2}+y^{2}-16 x-10 y+80=0$