Official Guide Explanation:
Problem Solving #212




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Solution and Metadata

Question: 212
Page: 182
Difficulty: 7 (Very Difficult)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Geometry > Circles > other

Explanation: You can think of OC as the hypotenuse of a triangle. If you draw a line straight down from C, perpendicular to the x - axis, and call that point on the x - axis X, your triangle is OCX. CX is a radius, and XO is equal to a radius--it's the same distance as a line drawn parallel to the x - axis between C and the y - axis. So, triangle OCX is an isoceles right triangle, which we know has sides of the ratio x:x:x rt[2]. Since k is the hypotenuse, k = x rt[2], or x = ((k)/( rt[2])). Since x is the length of a side of the triangle, and the side is a radius of the circle, that's our answer, choice (B).

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