Question 148486
First draw the inscribed triangle in the circle and label all of the sides and angles given. 


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/step1-4.jpg" alt="Photobucket - Video and Image Hosting">


Now draw in the radius from the center O to the angle ACB. Since the inscribed angle BAC is 45 degrees, this means that the central angle BOC is 90 degrees (remember the central angle is double the inscribed angle when they cut the same arc length). Now since the diameter is 12, this means that the radius is 6. So let's draw all of this info in:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/step2edit.jpg" alt="Photobucket - Video and Image Hosting">



Since OC is perpendicular to AB, this means that OC is the height and AB is the base



Now let's use the area of a triangle formula to find the area


{{{A=(1/2)*b*h}}} Start with the known formula



{{{A=(1/2)*12*6}}} Plug in {{{b=12}}} and {{{h=6}}}



{{{A=72/2}}} Multiply



{{{A=36}}} Reduce



So the area of the triangle is 36 square units. This means that the answer is choice d)