1) insuff coz you can form many triangles ABC with C and B are intersection points between any tangents to the circle with two sides of the angle A.

2) sorry, I can not attach my illustration ( in paint file) here.

As vikramm just edited the picture, A in my solution is indeed C in his picture and vice versa
You can easily prove that AE is indeed AD.

We have angle FOD= 360- (90+90+45) = 135 --->AOF= 180-135=45--->OAF= 445 or DAB= 45

We also have EAB=45

DAB=EAB= 45 -----> AD is indeed AE.

AD= sqrt 2, OD=1 ==> AD= 1+ sqrt 2

AD=1/2 BC ( Coz AB=AC ---> AD is also the median of right triangle ABC) ----> BC= 2*AD= 2+2*sqrt2

Area of ABC= AD*BC/2= (1+sqrt 2)^2

1 and 2 must be together to be sufficient to provide answer. C is correct.

NOTE:

You'd better open the doc file in seperate page so that you can understand my explanation. I'm badly sorry for my clumsy illustration coz I know no other means to draw some illustration.
Attachments

ABC.doc [24.5 KiB]

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