Mathematics Question and Solution
Calculating length EC.
Let it be x.
Let y be the radius of the blue inscribed circle.
It implies;
a = y+y+y+y
a = 4y units.
a is the diameter of the ascribed circle.
b²+(25+4)² = (4y)²
b² = 16y²-29²
b = √(16y²-841) units.
b is BC.
Calculating y.
25 ~ 29
y ~ √(16y²-841)
cross Multiply.
25√(16y²-841) = 29y
25²(16y²-841) = (29y)²
10000y²-525625 = 841y²
10000y²-841y² = 525625
9159y² = 525625
y = √(525625/9159)
y = 7.57554665261 units.
Again, y is the radius of the inscribed circle.
tanc = 25/y
c = atan(25/7.57554665261)
c = 73.1420439775°
c is angle AO¹E.
d = 180-c
d = 180-73.1420439775
d = 106.857956022°
d is angle CO¹E.
It implies x, length EC is;
x² = 2y²-2y²cosd
x² = 2(7.57554665261)²-2(7.57554665261)²cos106.857956022
x = √(2(7.57554665261)²-2(7.57554665261)²cos106.857956022)
x = √(148.063380281)
x = 12.1681296953 units.
Again, x is length EC.
