Mathematics Question and Solution
Calculating Area Yellow Circle.
Let r be the radius of the circle.
r² = 1²+a²-2acos135
r² = 1+a²+√(2)a --- (1).
r² = √(7)²+a²-2√(7)acos45
r² = 7+a²-√(14)a --- (2)
Calculating a.
Equating (1) and (2).
1+a²+√(2)a = 7+a²-√(14)a
(√(2)+√(14))a = 6
a = ½(√(14)-√(2)) units.
a = 1.1637219122 units.
Calculating r.
Recall.
At (1).
r² = 1+a²+√(2)a
And a = ½(√(14)-√(2)) units.
r² = 1+(½(√(14)-√(2)))+√(2)(½(√(14)-√(2)))
r² = 4
r = 2 units.
Yellow Ascribed Circle is;
πr²
= 4π square units.
