Let a triangle \( A B C \) be inscribed in the circle \( x^{2}-\sqrt{2}(x+y)+y^{2}=0 \) such tha... VIDEO
Let a triangle \( A B C \) be inscribed in the circle \( x^{2}-\sqrt{2}(x+y)+y^{2}=0 \) such that \( \angle B A C=\frac{\pi}{2} \). If the length of side \( A B \) is \( \sqrt{2} \), then the area of the \( \triangle A B C \) is equal to :
(a) 1
(b) \( \frac{(\sqrt{6}+\sqrt{3})}{2} \)
(c) \( \frac{(3+\sqrt{3})}{4} \)
(d) \( \frac{(\sqrt{6}+2 \sqrt{3})}{4} \)
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