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2019/20 AHSMC Part 1 Problem 1

Problem 1 of 16

Two circles C1C_1, C2C_2 have radius 66 cm and 88 cm, respectively. A third circle's area is the same as the sum of the areas of C1C_1 and C2C_2. The radius of the third circle in cm is

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Solution

C1C_1 has area 36π36\pi cm2^2 and C2C_2 has area 64π64\pi cm2^2. The sum of their areas is 100π100\pi cm2^2. Therefore, the radius of the third circle is 100=10\sqrt{100} = 10 cm. The answer is (A).

University of Alberta