<s>[INST] Area of triangle A triangle is inscribed in a circle. The vertices of triangle divide the circle into three arcs of length 3, 4 and 5 units, then find the area of triangle.
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Study the above diagram which describes the problem.
From the calculations of the arc lengths, we have:
$$3 = rA, \qquad4 = rB, \qquad 5 = rC$$
$$3 + 4 + 5 = rA + rB + rC = r(A + B + C)$$
$$r = \frac{12}{A + B + C} = \frac{6}{\pi}$$
We also know that the angles $A,B,C$ are in proportions corresponding to the respective arc length proportions. So, 
$$A = \frac{6\pi}{12}, \qquad B = \frac{8\pi}{12}, \qquad C = \frac{10\pi}{12}$$
I believe it is easy to compute the area of the inscribed triangle from here: It is given by
$$\frac{1}{2}r^2\sin A + \frac{1}{2}r^2\sin B + \frac{1}{2}r^2\sin C$$
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