In an isosceles triangle \( O A B, O \) is the origin and \( O A=O B \) \( =6 \). The equation o...

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In an isosceles triangle \( O A B, O \) is the origin and \( O A=O B \) \( =6 \). The equation of the side \( A B \) is \( x-y+1=0 \). Then the area of the triangle is
(A) \( 2 \sqrt{21} \)
(B) \( \frac{\sqrt{142}}{2} \)
(C) \( \sqrt{142} \)
(D) \( \frac{\sqrt{71}}{2} \)
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