Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
4th June, 2025

Let a be the radius of the red inscribed circle.


b = (4-a) units.


tan30 = a/b

⅓√(3) = a/(4-a)

3a = 4√(3)-√(3)a

(3+√(3))a = 4√(3)

a = 4√(3)/(3+√(3))

a = ⅙(12√(3)-12)

a = (2√(3)-2) units.

a = 1.46410161514 units.


Therefore, area red inscribed circle is;


πa²

= π(2√(3)-2)²

= π(12-8√(3)+4)

= (16-8√(3))π

= 8(2-√(3))π square units.

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