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Intermediate

The rising sun

A rectangle with a circle and a semicircle. What is the proportion red : blue in terms of a and b?

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Solution

The proportion red : blue is 2(1-a/2b)2.

Solution by علاء و م.

Poem

The rising sun
The sun rises through windows and curtains
We are alive in our homes
We are in peace
We have no war
We can see the moon
We can feel the sun
We smell no blood
So sad feelings
And place for death
We will all have hope
In our world
When does this battle end ?

Bella

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One reply on “The rising sun”

Using similar triangles involving tangents to the blue semicircle and red circle, then a bit of algebra, it can be easily (!) shown that the ratio of RED to BLUE is [(2b-a)^2]/[2b^2].

The minimum allowed value for b is a/2 when the red circle disappears and R/B is zero.

As b tends to infinity, R/B tends to 2.

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