NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 54 of 100

Marks: +1, -0

Two circles, both of radii a touch each other and each of them touches internally a circle of radius 2a. Then the radius of the circle which touches all the three circles is

$1/2a$
$2/3a$
$3/4a$
a

Validate

Solution:

Since, in figure, AAOB is a right angled triangle

∴OA^{2}=AB^{2}+OB^{2}

⇒(a+r)^{2}=(2a-r)^{2}+a^{2}

⇒a^{2}+2ar+r^{2}=4a^{2}+r^{2}-4ar+a^{2}

⇒6ar=4a^{2}⇒r=\;\;{2a}/{3}

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