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
2 years, 11 months 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

- 1 year ago

nice job and they are congruent

- 11 months, 3 weeks ago

not similar

- 11 months, 3 weeks ago

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

- 2 years, 11 months ago

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

- 2 years ago

You are right but

- 2 years, 10 months ago

Prove it

- 2 years, 10 months ago

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.

- 2 years ago