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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} $. 📰 5 Transform Surveys Fast Heres How Microsoft Forms Multiple Choice Changes Everything 5609593 📰 The Hidden Hack Only Real Smile Login Users Know 366048 📰 When Do Nba Finals Start 488356 📰 Star Ocean The Divine Force Walkthrough 1789568 📰 Breathless Naked Shot Of Megan The Stallion Leaves Fans Speechless 1754347 📰 Years Later The Alpha Zombie Returns Unbelievable Transformation Revealed 1734347 📰 Surprised What These Good Games To Play Online Really Deliverfinal Top Picks 7134281 📰 Charles Old Train Ride Reveals Secrets No One Expected 6378515 📰 Cast Of People We Meet On Vacation Film 5297063 📰 You Wont Believe The Courage Behind Superman Man Of Steels Legacy 8293289 📰 Life In Prison Roblox 1012160 📰 The Ultimate Guide To Usa Poverty Guidelinesare You Living Under The Poverty Line 6634126 📰 Dont Miss This Shocking Method To Shut Down Your Pc Instantly Safely 6136772 📰 5 Your Ultimate Mp3 Downloader Hackdownload Proven Tools Instantly 697545 📰 The Ultimate Chicken Big Mac Threat Is It Really Worth The Bite Street Shocking Reveal 701097