A = c \cdot s,

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• A = \frac{1}{2}ab.
• The inradius \( c \) of a right triangle is given by:
• where \( z = \sqrt{a^2 + b^2} \). Also, the area can express in terms of the inradius:
• where \( s = \frac{a + b + z}{2} \) is the semi-perimeter.
• A_{\text{circle}} = \pi c^2.
• Thus, the ratio \( R \) of the area of the circle to the area of the triangle is:

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