Question

A line is touching two circles at T₁ and T₂, respectively, such that the length T₁T₂ is 36. The minimum distance between the circles is 14. If the radius of the larger circle is four times the radius of the smaller circle, then the radius of the smaller circle is

(A)  5

(B)  4

(C)  3

(D)  10

Answer 1

Correct option  (A) 5 

Explanation :

Points A and B are the centres of the two circles. PQ = 14 and T₁T₂ = 36. Draw T₁M parallel to AB to BT₂ (see Fig.). Let r and 4r be the radii. From Δ T₁T₂M, we have (T₁M)₂ = (T₁T₂)² + (T₂M)². Therefore,