BC = √(√(3)²+1²)
BC = 2 units.
Let r be the radius of the circle.
Using similar triangles ratio rule on triangle ACE and triangle BCE to calculate r.
1 = √(3)
√(3) = AE
Cross Multiply.
AE= 3 units.
Therefore;
r = ½(AE+BE)
r =½(3+1)
r = 2 units.
Angle ADC is;
180-atan(√(3))
= 180-60
= 120°
Therefore shaded area or area triangle ACD is;
½*2*2sin120
= 2sin120
= √(3) square units.
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