AMO 2027 Grades 10-12 SET 2 - Self-study Question 8

In the adjoining figure, if the value of the larger 2 circles is 72 and 18, find the radius of the smallest circle. All circles are tangent to each other and to the common ray $B$.



**Editorial clarification.** Interpret the unspecified values 72 and 18 as the radii of the two larger circles. Use the externally tangent configuration on one side of the ray shown in the figure, with the smallest circle in the intervening gap.

Choose one option.