Mathematics Question and Solution
Calculating Area ADCB, a Cylic Quadrilateral.
a = ½(45)
a = 22.5°
a is angle CBD.
b = a+45
b = 22.5+45
b = 67.5°
b is angle ABE.
sin67.5 = 10/c
c = 10.8239220029 units.
c is AB = AD.
d² = 2c²
d² = 2*10.8239220029²
d = √(2*10.8239220029²)
d = 15.3073372946 units.
d is BD, the diameter of the circle.
cos22.5 = e/15.3073372946
e = 15.3073372946cos22.5
e = 14.1421356237 units.
e is BC.
sin22.5 = f/15.3073372946
f = 15.3073372946sin22.5
f = 5.85786437626 units.
f is CD.
It implies, area ADCB, a cylic quadrilateral is;
½(10.8239220029*10.8239220029)+½(14.1421356237*5.85786437626)
= 58.5786437624+41.4213562372
= 100 square units.
