Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 693.

## Thursday, November 24, 2011

### Problem 693: Square, Inscribed and Circumscribed Circle, Areas, Mind Map, Polya

Labels:
area,
circle,
circumscribed,
George Polya,
inscribed,
mind map,
square

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Let OC = R so FG = R & SQUARE HEFG = R^2.

ReplyDeleteFurther, OG = CG = R/√2 so inner circle =(∏R^2)/2 and the blue corner FCG = R^2/2 -(∏R^2)/8

Thus, total blue area= 4[R^2/2 -(∏R^2)/8]+2[(∏R^2 -2R^2)/4]=R^2 on simplification. Hence etc.

Ajit