2009/10 AHSMC Part 1 Problem 14

Problem 14 of 16

A chord of a circle divides the circle into two parts such that the squares inscribed in the two parts have areas $16$ and $144$ square centimetres. In centimetres, the radius of the circle is

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Solution

Let $x$ be the distance from the centre of the circle to the bottom edge of the larger square. The square of the radius of the circle is given by $6^2 + x^2 = 2^2 + (4 + 12 - x)^2$ . This yields $x = 7$ so that the radius of the circle is $\sqrt{6^2 + 7^2} = \sqrt{85}$ . The answer is (D).

University of Alberta

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