A right triangle is inscribed in a circle with a diameter $100$ units long. What is the maximum area of the triangle, in square units?
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<|im_start|>user
A right triangle is inscribed in a circle with a diameter $100$ units long. What is the maximum area of the triangle, in square units?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2500
A right triangle is inscribed in a circle with a diameter $100$ units long. What is the maximum area of the triangle, in square units?
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