Geometry Problem

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

Click the figure below to see the complete problem 697.

## Saturday, December 3, 2011

### Problem 697: Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map

Labels:
area,
circle,
circular sector,
circular segment,
congruence,
square

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Let the big circle touch AB & BC in P & T resply. Let OB intersect the big circle in Q & R resply. Let A1 =area BQT, A2 = area PQR and A3 = sector RO. The white area = 4(A1+A2+A3).

ReplyDeleteNow we let OE=x and hence S=16x^2. Further, it's simple to show that A2=A3=(∏x^2-2x^2)/4 and A1=2x^2-∏x^2/2 which makes the total white area=2(∏x^2-2x^2)+ (8x^2-2∏x^2)=4x^2 or the yellow area =12x^2=3S/4

Correction in the proof above: Let the big circle and the small left circle intersect OB in Q & R resply.

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