AB is a common tangent to both the circles in the given figure. Find the distance (correct to two decimal places) between the centres of the two circles.

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \Rightarrow \text{By figure,}\\ & \Delta CAE\sim \Delta DBE\\ & \frac{CA}{BD}=\frac{AE}{BE}\\ & \frac{5}{x}=\frac{8}{12}\\ & x=7.5=\left(\frac{15}{2}\right)\\ & \Rightarrow \text{Length of T}\text{.L}=\sqrt{d^2-{\left(R_1+R_2\right)}^2}\\ & {\left(20\right)}^2=d^2-{\left(5+7.5\right)}^2\\ & 400=d^2-156.25\\ & d^2=400+156.25\\ & d^2=556.25\\ & d=\sqrt{556.25}\\ & d=23.58\end{array}$$