Something to lighten the mood

Here is a variant of puzzle at post #1268.

Same but with 16 80 instead of 24 100.
Then it is more of a challenge to find the area of the circle.

Enjoy.
It is 4.8 with the same logic as I described before.
The sides of the triangle are 4 and 8, the hypotenuse is 4 x sqrt(5), and the radius of the circle is 6 - 2*sqrt(5)
It is interesting that one gets a finite decimal by multiplying two infinite decimals.
 
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It is 4.8 with the same logic as I described before.
The sides of the triangle are 4 and 8, the hypotenuse is 4 x sqrt(5), and the radius of the circle is 6 - 2*sqrt(5)
Indeed the radius is 6 - 2*sqrt(5) that can be written 6 - sqrt(20) the answer of Mark.
It is interesting that one gets a finite decimal by multiplying two infinite decimals.
I do not understand this comment neither your 4.8. The area of the circle is Pi*(56 - 24*sqrt(5))
 
I asked three people what pi is:

Geometrician: The ratio of a circle’s circumference to its diameter.
Mathematician: 3.14159265…
Engineer: About 3

Have a look to the "Indiana pi bill" an attempt to give an easy value for Pi. With 3.2 proposed.
I was told Pi=3 had been made by law in a Texan county. But, I can be wrong.
Do not confuse with PI ( Public Intoxication ) laws.
 
In college days, I remember several fellow students who proudly memorized pi to ten or fifteen or more decimal places.

For most practical purposes, "3.14" or "22/7" can be adequate, but one math professor gave a ratio that yielded 6 decimal place accuracy -- and was easy to remember.

Take the first 3 odd digits (1, 3, 5).
Begin writing in the denominator, from left to right.
Write each digit twice in order, with 3 figures in denominator, and the last 3 in the numerator.

355
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113