Two circles have centres a distance d apart. The direct common tangent has length L and the transverse common tangent has length M. Given that L^2 + M^2 = 320 and the sum of the squares of the two radii is 160, find d.

Question

Accepted Answer

8 root 5. Using L^2 = d^2 - (r1 - r2)^2 and M^2 = d^2 - (r1 + r2)^2, their sum is 2d^2 - 2(r1^2 + r2^2) = 320. With r1^2 + r2^2 = 160, we get 2d^2 - 320 = 320, so d^2 = 320 and d = 8 root 5.

Two circles have centres a distance d apart. The direct common tangent has length L and the transverse common tangent has length M. Given that L^2 + M^2 = 320 and the sum of the squares of the two radii is 160, find d.

Solution

Related SSC CGL (Prelims) General questions