1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider two circles in a plane with radii 5 and 3 respectively. Distance between centres of these two circles is 10 . If R1 is radius of circle passing through 4 points of contact of direct common tangents of these two circles and R2 is radius of circle passing through 4 points of contact of transverse common tangents then ( mathrmR1/ mathrmR2)= ?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider two circles in a plane with radii 5 and 3 respectively. Distance between centres of these two circles is 10 . If $R_1$ is radius of circle passing through 4 points of contact of direct common tangents of these two circles and $R_2$ is radius of circle passing through 4 points of contact of transverse common tangents then $\frac{\mathrm{R}_1}{\mathrm{R}_2}=$ ?

JEE AdvancedJEE Advanced 2019

Solution:

image
$ \mathrm{FG}=\frac{\mathrm{r}_1+r_2}{2} $
$ \mathrm{~GB}=\sqrt{(F G)^2+(F B)^2}$
$ (\mathrm{~GB})^2=\frac{\left(r_1+r_2\right)^2}{4}+\frac{d^2-\left(r_1-r_2\right)^2}{4} $
$ =\frac{d^2+4 r_1 r_2}{4}$
$ R_1^2=\frac{\left(C_1 C_2\right)^2+4 r_1 r_1}{4}=40 $
$ R_2^2=\frac{\left(C_1 C_2\right)^2-4 r_1 r_1}{4}=10$