## Geometry – Circle Area

*April 28, 2016 at 12:29 am* *
2 comments *

Illustrated below is a quarter-circle, containing two semicircles of smaller circles. Prove that the red segment has the same area as the blue.

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1.M | July 15, 2016 at 2:22 pmRed = All – 2 * SmallHalf + Blue

All = 1/4 * 2 * PI * R^2

SmallHalf =1/2 * 2 * PI *(1/2 * R)^2

-> Red = (1/4 * 2 * PI * R^2) – 2 * (1/2 * 2 * PI *(1/2 * R)^2) + Blue

Red = 1/2 * PI * R^2 – 2 * 1/4 *PI *R^2 + Blue

Red = PI * R * (1/2 – 2/4) + Blue

Red = Blue

Q.E.D.

2.squarepi | July 15, 2016 at 2:36 pmThanks for stopping by. This was a cool problem that I’m hoping to share with my students.

Solid solution too!