Question

An oblique triangle is inscribed in a circle. If one side of the triangle having a length of 10 cm and the angle subtended to that side is 20. Determine the area of the circle.

Answer 1

if you mean the angle is 20°, then the radius r of the circle can be found using'

5/r = sin10°

Now you know r, so you can find the area of the circle...

Answer 2

10/d=sin(20)
A=(pi(d)2)/4
ans.A=671.4 sq. unit

Answer 3

The solutions above are wrong.
sin A = opposite / hypotenuse

We know the angle A = 20 and hypotenuse = 10 cm
Therefore:

Sin 20 = O/ 10
O =3.42 cm

Since circle is inscribed in the triangle, the opposite side is the diameter. D = 3.42 cm so it makes R = 1.71 cm

Area of circle is pi * r²
A = 9.18 cm²

Answer 4

This problem can be solved using sine law.
By drawing the figure, an oblique triangle is inside the circle

then the angle opposite to its side is 20° , then the subtended angle towards the center of the circle is θ=2θ; 2(20°)= 40°
using summation of the interior angle, 180°= 40 ° + x° + x°
x = (180° - 40°)/2 = 70°
the two remaining angles are both 70 °

using sine law:
(10/sin 40°) = (r/sin 70°)
r =14.6190 cm

then using the formula of an area of a circle:
A = πr²
A = π(14.6190)²
A = 671.4080 cm²