Mathematics Question and Solution
Let the radius of the ascribed circle be 2 units.
sin10 = a/2
a = 0.34729635533 units.
a is O1D.
cos10 = b/2
b = 1.96961550602 units.
b is CD.
Let the small inscribed circle radius be r.
Calculating r.
(2-r)² = r²+(0.34729635533+r)²
4-4r+r² = r²+0.12061475843+0.69459271066r+r²
r²+4.69459271066r-3.87938524157 = 0
It implies;
r = 0.716881 units.
c = 2-0.34729635533
c = 1.65270364467 units.
c is BD.
tand = 1.65270364467/1.96961550602
d = 40°
d is angle BCD.
tane = 0.716881/1.96961550602
e = 20°
e is angle DCP.
Therefore;
Angle PCB is;
d-e
= 40-20
= 20°
