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📰 In a right triangle, the length of one leg is \( a \), the length of the other leg is \( b \), and the length of the hypotenuse is \( c \). If the radius of the inscribed circle is \( r \), find the ratio of the area of the circle to the area of the triangle. 📰 The area of the triangle is given by \( \frac{1}{2}ab \). The semi-perimeter \( s \) of the triangle is \( \frac{a + b + c}{2} \). The radius of the inscribed circle \( r \) can be expressed as \( r = \frac{A}{s} \), where \( A \) is the area of the triangle. Therefore, \( r = \frac{\frac{1}{2}ab}{\frac{a + b + c}{2}} = \frac{ab}{a + b + c} \). The area of the inscribed circle is \( \pi r^2 \). Substituting for \( r \), the area of the circle is \( \pi \left(\frac{ab}{a + b + c}\right)^2 \). The ratio of the area of the circle to the area of the triangle is: 📰 \frac{\pi \left(\frac{ab}{a + b + c}\right)^2}{\frac{1}{2}ab} = \frac{2\pi a^2b^2}{(a + b + c)^2 ab} = \frac{2\pi ab}{(a + b + c)^2} 📰 Words That Begin With U N 6649578 📰 Can This Xrp Wallet Change Your Crypto Game Overnight Find Out 5123636 📰 Apple Watch Charger 2413155 📰 Basket Battle Tour The Unmatched Showdown That Will Shock You 2819958 📰 How Many Kids Does Donald Trump Have 4330975 📰 Free Black Porn Sites 9917108 📰 Five Guys Nutrition 1194622 📰 Spider Ham Alert The Creepy Snack Taking Social Media By Storm 1789786 📰 This Sexy Hot Secret Is Taking The Web By Stormare You Ready 7691742 📰 The Robot Returns To Its Starting Orientation After 12 Iterations 9860460 📰 Helldivers Companion Why Every Gamer Deserves One In 2025 3026880 📰 Stack Ball Hacks That Are Going Viralwatch How It Transforms Your Setup 757992 📰 Inn At The Convention Center 8838245 📰 30A Florida Real Estate 7033165 📰 Best Home Warranty Company Texas 9343104