# 2018 AMC 12B Problems/Problem 4

## Problem

A circle has a chord of length 10, and the distance from the center of the circle to the chord is 5. What is the area of the circle? $\textbf{(A) }25\pi \qquad \textbf{(B) }50\pi \qquad \textbf{(C) }75\pi \qquad \textbf{(D) }100\pi \qquad \textbf{(E) }125\pi \qquad$

## Solution

The shortest segment that connects the center of the circle to a chord is the perpendicular bisector of the chord. Applying the Pythagorean theorem, we find that $$r^2 = 5^2 + 5^2 = 50$$ The area of a circle is $\pi r^2$, so the answer is $\boxed{\text{(B)} 50\pi}$

## See Also

 2018 AMC 12B (Problems • Answer Key • Resources) Preceded byProblem 3 Followed byProblem 5 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions

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