NTSE Stage 2 SAT 2016 Question Paper

Question : 55 of 100

Marks: +1, -0

Three circles with radii

R_1 , R_2

and r touch each other externally as shown in the adjoining figure. If PQ is their common tangent and

R1 > R2

, then which of the following relations is correct ?

Solution:

\PR=√{(\R_1+\r)^2-(\R_1-\r)^2}

=√{4\R_1\r}

.....(1)

\RQ=√{4\R_1\r}

....(2)

\PQ=√{4\R_1\R_2)}

....(3)

\PQ = \PR + \RQ

⇒

√{4\R_1\R_2}=√{4\R_1\r_2}+√{4\R_2\r}

√{\R_1\R_2}=√{\R_1\r}+√{\R_2\r}

1/√\r=1/√\R_2+1/√\R_1

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