Question

Two circles with centres O and N touch each other at the point P as shown in the figure. O, P and N are collinear. Radius of the circle with centre O is twice that of the circle with centre N. OX is tangent to the circle with centre N and $OX = 18	ext{ cm}$. The radius of the circle with centre N is :

Accepted Answer

C. Let radius of circle N be $r$. Then radius of circle O is $2r$. Distance $ON = OP + PN = 2r + r = 3r$. Since OX is tangent to circle N at X, $\angle OXN = 90^\circ$. In right $	riangle OXN$: $$ON^2 = OX^2 + NX^2 \implies (3r)^2 = 18^2 + r^2 \implies 8r^2 = 324 \implies r^2 = \frac{81}{2} \implies r = \frac{9}{\sqrt{2}}	ext{ cm}$$

Radius of touching circle with tangent

Explanation

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