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PIMSO 2022 - Mathematics - Grade 10 / Secondary 4 - National Round Question 21

PIMSO Maths · PIMSO 2022 - Mathematics - Grade 10 / Secondary 4 - National Round

Question 21

Given the figure below, the distance between the center of the 2 identical bigger circles is given by x while their radii are given by R. If the radius of the smallest circle at the top is given by r, what is the shortest distance from the center of the topmost circle to line m?

Question illustration

Use the external tangencies shown. Enter an expression in R,r,x; use sqrt(...) for square root.