Mathematics Question and Solution
Let r be the radius of the circle.
It implies, calculating r.
r² = (r-1)²+(r-0.5)²
r² = r²-2r+1+r²-r+(¼)
0 = r²-3r+(5/4)
4r²-12r+5 = 0
Resolving the above quadratic equation via completing the square approach to get r, radius of the circle.
r²-3r = (-5/4)
(r-(3/2))² = (-5/4)+(-3/2)²
(r-(3/2))² = (-5/4)+(9/4)
(r-(3/2))² = 1
r = (3/2)±1
It implies;
r ≠ (3/2)-1
r = (3/2)+1
r = 2.5 cm.
Notice!
The blue area is a square.
Therefore, a, side length of the square is;
a = 2r-1
a = (2*2.5)-1
a = 5-1
a = 4 cm.
It implies, blue area (area Blue square) is;
a²
= 4²
= 16 cm²
