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Geometry Level 3

$ABC$ is an equilateral triangle. $EB = 2CE$ . $D$ is chosen to maximize the area of $\triangle DFE$ . Which circle is larger, yellow or red? No guessing allowed! Counting pixels, however, is encouraged.

Red Yellow Yellow and Red are equal

2 solutions

Hosam Hajjir
Jun 7, 2021

The maximum area blue triangle is achieved when $\dfrac{AD}{AC} = \sqrt{6} - 2$ . Taking a unit equilateral triangle, we can compute the radii of the red circle and the yellow circle, they are given by

$r_\text{red} \approx 0.1448789$

$r_\text{yellow} \approx 0.1465026$

Hence, the yellow circle is larger.

Maria Kozlowska
Jun 7, 2021

I guess there is going to be social distancing on Brilliant.

"As of July 2, 2021, we will not be accepting new community problem submissions, or solutions on those problems, and the community section will be removed from Brilliant. We will also not be accepting new explanation submissions on Daily Challenges."

This is very sad news. Some guys are trying to get organized and move Brilliant community elsewhere. I hope that will work.

Very sad and disappointing news indeed. Maria, let us know if we can help in any way for an effort to keep the community in touch. I don't know how to get this information.

Thanos Petropoulos - 5 days, 2 hours ago

here

Maria Kozlowska - 5 days, 2 hours ago

Thanks! I see efforts by many community members, this is good. I hope @Chew-Seong Cheong will make it with his tries.

Thanos Petropoulos - 4 days, 12 hours ago

mention[5506640:Thanos Petropoulos],mention[1153645:Maria Kozlowska]

Agent T - 4 days, 16 hours ago

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