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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} 📰 Roblox Mcdonalds Tycoon 📰 Question A Climate Resilience Educator Is Designing A Modular Shelter System Where Each Structure Must Be Built Using Exactly 48 Beams And 72 Poles What Is The Maximum Number Of Identical Shelters That Can Be Constructed Using All The Resources 3634426 📰 Nds Emu For Pc 3625658 📰 Moroccan Dirham Near Me 📰 Stock Losers Today 📰 Did Abraham Lincoln Have Slaves 📰 Crazy Flips 📰 Discover The Best Free Game Websites Thatll Keep You Entertained Forever 1524574 📰 Bank Of America Bonney Lake Washington 📰 Robert Kiyosaki 📰 Bree Fowler Cnet 📰 Get Windows 7 64 Bits On Tapdownload It Now Reclaim Your Old Pc 4789204 📰 Bank Of America Gambrills 📰 Zerowater 10 Cup 5 Stage Pitcher 27374 📰 Uta Email 4880062