Question

Two circles with radii 9 cm and 4 cm touch each other externally. Find the radius of a circle which touches these two circles as well as a common tangent of the two circles

Answer 1

Answer:

12

Step-by-step explanation:

length of direct common tangent

=√d²-(r1-r2)²

distance between two circle=9+4=13

r1=9 ,r2=4

√13²-(9-4)²=√169-25=√144=12

Answer 2

The radius of the circle touching the two circles and also common tangent of given circles is 36/25 cm.

• We know that,

            "If two circles with radii a and b touch each other externally, then radius of the circle which touches these two circles as well as a common tangent of these circles is given by

                       $\frac{1}{\sqrt{c} }=\frac{1}{\sqrt{a} }+\frac{1}{\sqrt{b} }$

• Here,

                    a = 9 cm, b = 4 cm

                    $\frac{1}{\sqrt{c} }=\frac{1}{\sqrt{9} }+\frac{1}{\sqrt{4} }\\  \frac{1}{\sqrt{c} }=\frac{1}{3}+\frac{1}{2}\\   \frac{1}{\sqrt{c} }=\frac{2+3}{6}\\ \frac{1}{\sqrt{c} }=\frac{5}{6}\\\sqrt{c}=\frac{6}{5}\\ c=\frac{36}{25}$