2018 AMC 12B Problem #4

Geometry Level 2

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?

This problem is part of the 2018 AMC 12B .
125 π 125 \pi 100 π 100 \pi 50 π 50 \pi 75 π 75 \pi 25 π 25 \pi

Steven Yuan by Steven Yuan , 20, USA

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1 solution

Kevin Tran
Feb 16, 2018

A = π r 2 A = π ( 5 2 ) 2 A = 50 π A\quad =\quad \pi { r }^{ 2 }\\ A\quad =\quad \pi { (5\sqrt { 2 } ) }^{ 2 }\\ A\quad =\quad 50\pi

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