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First, complete the circle. Draw BD and join one of its end D to C. ∠BAC + ∠BDC= 180° ∠D = 40°, ∠BCD (angle on semicircle).
So ABCD is right-angled.
sin 40 = \(\frac{8}{BD}\)
BD = \(\frac{8}{sin\,40}\) = \(\frac{8}{0.6428}=12.44\)
Radius = \(\frac{12.4}{2}\) = 6.2 cm