In figure shown, radius of circle C₁ be r and that of C₂ be frac{r}{2} , where r= frac {1}{

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10-1.Circle and System of Circles

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In the figure shown, radius of circle $C_1$ be $ r$ and that of $C_2$ be $\frac{r}{2}$ , where $r= \frac {1}{3} PQ,$ then length of $AB$ is (where $P$ and $Q$ being centres of $C_1$ $\&$ $C_2$ respectively)

A

$2 \sqrt {3} r$

B

$\frac{3 \sqrt {3} r}{4}$

C

$3 \sqrt {3} r$

D

$\frac{3 \sqrt {3} r}{2}$

Solution

$AB = \sqrt {{{\left( {PQ} \right)}^2} – {{\left( {r – \frac{r}{2}} \right)}^2}} $

$ = \sqrt {9{r^2} – \frac{{9{r^2}}}{4}} $

$ = \frac{{3\sqrt 3 }}{2}r$

Standard 11

Mathematics

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