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## Official Guide Explanation:Problem Solving #212

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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