Mock test 1 - Q10 - pending

Q10. Two circles with radii 4 and 9 respectively touch each other externally. Let c be the radius of a circle that touches these two circles as well as a common tangent to the two circles. Find 25c = ?
Solution:

Use 
https://en.wikipedia.org/wiki/Descartes%27_theorem

(k1 + k2 + k3 + k4)^2 = 2(k1^2 + k2^2 + k3^2 + k4^2)
Here k4 = 0 for the straight line(0 curvature).
k1 = 1/4, k2 = 1/9, k3 = 1/c
It's a quadratic in k3.
You will get k^2 - 26k/36 + 25/36^2 = 0.
It has 2 solutions k = 1/36,25/36 => c = 36,36/25 
Radius can't be 36 as seen in the diagram.
So 25c = 36.







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