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📰 Solution: The area of the incircle is $ \pi c^2 $. For a right triangle, the semiperimeter $ s = \frac{a + b + z}{2} $, and the inradius $ c = \frac{a + b - z}{2} $. The area of the triangle is $ r \times s = c \times (z + c) $. Therefore, the ratio is $ \frac{\pi c^2}{c(z + c)} = \frac{\pi c}{z + c} $. The answer is $ \boxed{\dfrac{\pi c}{z + c}} $. 📰 Question: A robotics researcher designs a circular obstacle avoidance path for a robot. If the robot's shortest detour forms a triangle with sides of 7 units, 24 units, and 25 units, what is the radius of the circumscribed circle around its path? 📰 Solution: For a right triangle with legs 7 and 24, and hypotenuse 25, the hypotenuse is the diameter of the circumscribed circle. The radius $ r = \frac{25}{2} = 12.5 $ units. Thus, the radius is $ \boxed{12.5} $. 📰 Soundflower Download Mac Os X 6707013 📰 Dogs Chia Seeds The Secret Superfood Youve Been Missing 7515297 📰 You Wont Believe How Easy This Card Ladder Clears Your Living Roomtry It Now 6303779 📰 Bank Of America Void Check For Direct Deposit 8362866 📰 Guilty Plea These Hidden Jobs Pay Teens Fast 3599216 📰 Shocking Fix Oracle And Vmware Licensing Secrets That Could Save Your Business Billions 892380 📰 Creator Portal 8171053 📰 Master Rounding In Excel The Secret Shortcut You Cant Ignore 2270272 📰 Discover The Secret Ingredient Hiding In Every Sip At Your Fav Cocktail Bar 2665963 📰 John Reeves 7470732 📰 Activation Code Leaked Heres The One That Unlocks Instant Access 1363534 📰 This Hidden Lie In The Broken Arrow Movie Will Have You Watching Until The Endclicks Increase By 800 9643510 📰 Reader Wont Believe What This Edible Printer Can Make You Eat 5907103 📰 Open Ai Careers 1047847 📰 Why Is Gold Tanking Today 8553197