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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} 📰 You Wont Believe What Happens After You Log Infactor Secrets Revealed 9252345 📰 What Is Patriots Day Holiday 5673880 📰 Green Beans Cultivation Like A Pro Secrets You Need To Know 2289562 📰 Bridal Hair 1813841 📰 Chinese Zodiac Of 1994 9699673 📰 Unlock Your Biggest Prizesget The New York Lottery App Instantly 9196800 📰 A Green Chemistry Lab Runs A Series Of Continuous Flow Reactions Using 4 Parallel Reactors Each Reactor Processes 32 Liters Per Minute If The Experiment Runs For 25 Hours How Many Total Liters Are Processed 2117353 📰 Dream Big Moondragons Hidden Powers Are About To Change Everything 4373664 📰 Wells Fargo Fernley 5402191 📰 Wwe Summerslam 2025 2796364 📰 Football Background 1746610 📰 Finally Stop Emails When Youre Gonestep By Step Guide To Set Your Outlook Out Of Office 739463 📰 My Brilliant Friend Cast 5413970 📰 Water Hazard Drink Shock This Crazy Beverage Dwarfs All Hydration Trends Try It Now 4457134 📰 This Forgotten Song From Decades Ago Has Sparked A Massive Online Revival 1807214