The area $A_{\text{triangle}}$ of a right triangle with legs $a$ and $b$ and hypotenuse $t$ is:
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- Question: A right triangle has a hypotenuse of length $t$, and the radius of the inscribed circle is $r$. What is the ratio of the area of the circle to the area of the triangle?
- Solution: The area $A_{\text{circle}}$ of the inscribed circle is:
- A_{\text{triangle}} = \frac{1}{2}ab
- The radius $r$ of the incircle of a right triangle is given by:
- r = \frac{a + b - t}{2}
