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}.

## 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 ?

## 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.