Inscribed Circle

Algebra Level 2

The area of the circle inscribed in the graph x 2 + y 7 = 12 |x-2|+|y-7|=12 is a π . a\pi. What is the value of a ? a?

64 80 56 72

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1 solution

Tom Engelsman
Nov 7, 2020

The graph x 2 + y 7 = 12 |x-2|+|y-7|=12 represents a square with vertices at ( x , y ) = ( 2 , 5 ) ; ( 2 , 19 ) ; ( 10 , 7 ) ; ( 14 , 7 ) (x,y) = (2,-5); (2,19); (-10,7); (14,7) and side length of 12 2 . 12\sqrt{2}. The inscribed circle has an area equal to:

A = π 4 d 2 = π 4 ( 12 2 ) 2 = 72 π . A = \frac{\pi}{4}d^2 = \frac{\pi}{4}(12\sqrt{2})^2 = \boxed{72\pi}.

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