Mathematics Question and Solution
Radius of the circle r, is;
πr² = 25π
r = 5 cm.
Therefore diameter is;
2r
= 10 cm.
Let the side of the small yellow Inscribed square be x.
a² = 2x²
a = √(2)x cm.
Where a is a diagonal of the small yellow Inscribed square.
Extending a.
We now have a rectangle inscribed the circle (cyclic quadrilateral) with diameter 10 cm.
Where 6 cm is the width and (6+√(2)x) cm is the length.
Calculating x (small yellow Inscribed square length)
10² = 6²+(6+√(2)x)²
100-36 = (6+√(2)x)²
8 = 6+√(2)x
2 = √(2)x
x = √(2) cm.
Area small yellow Inscribed square is;
x²
= √(2)²
= 2 cm²
