Find The Area

The blue and white circles combined have half the area as the outside circle. What is the area of the red part relative to the area to the whole circle?

Note: The parts are formed by lines tangent to the white circle and when the borders between colors are extended, it forms an equilateral triangle.

Note by Alex Wang
1 year, 11 months ago

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Is it not 1/3*1/2=1/6? Or you mean full white circle + full blue circle?

Saya Suka - 1 year, 11 months ago

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You are right but

Alex Wang - 1 year, 11 months ago

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Prove it

Alex Wang - 1 year, 11 months ago

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The red part, green part, and yellow part must all have an equal area. This is simply because of symmetry and someone who is not as lazy as I am can prove it in full. The total area of these consists of half of the full logo. This means that it is 1/3 of 1/2 or 1/6 as said by Saya Suka.

Ayush Kumar - 1 year, 1 month ago

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If that had been the case then I'm pretty the sure that there would be multiple answers.

Ayush Kumar - 1 year, 1 month ago

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yeah its just as simple as half the area of the big circle divided by three because each of those coloured sections out side the white and blue circle combined are congruent figures

Krishna Venkatraman - 1 month, 1 week ago

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nice job and they are congruent

Alex Wang - 1 week, 6 days ago

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not similar

Alex Wang - 1 week, 6 days ago

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