Question

Circles of radii 36 and 9 touch externally. The radius of the circle which touches the two circles externally and also their common tangent is

Answer 1

The radius of the circle is 4 cm.

• If there are two circles with radii a and b touching externally, then the radius of the circle which touches the two circles externally and also their common tangent is given by

                        $\frac{1}{\sqrt{c} } = \frac{1}{\sqrt{a} } +\frac{1}{\sqrt{b} } \\Here,\\a = 36 cm, b = 9 cm\\\frac{1}{\sqrt{c} } = \frac{1}{\sqrt{36} } +\frac{1}{\sqrt{9} } \\\frac{1}{\sqrt{c} } = \frac{1}{6} +\frac{1}{3} \\\frac{1}{\sqrt{c} } = \frac{1+2}{6} \\\frac{1}{\sqrt{c} } = \frac{1}{2} \\\sqrt{c} = 2\\c=4 cm$