Think Outside of the Circle

Geometry Level 2

Which figure has the largest area shaded in black?

Note: All the circles edges are touching to the side of the square or another circle and all the squares are congruent.

A Impossible to determine C All of them have the same area B

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2 solutions

Parth Sankhe
Nov 27, 2018

Both A and B have smaller identical C's fitted inside them. Hence, if the ratio of white area to black area in C is r r , the same ratio will be present in both A and B, since they are entirely made up of C's.

All have the same area of L 2 π ( L 2 4 ) = L 2 ( 1 π 4 ) L^2 - π(\dfrac {L^2}{4}) = L^2(1 - \dfrac π4)

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