Geometry · Reflection · Shortest path · Optimization · Pythagorean theorem · Ellipse
Problem 1, 1996
Two vertical poles stand on level ground, at a distance of \(9\) m from each other; one pole is \(11\) m high and the other is \(15\) m high. A rope of length \(15\) m is fastened to the top of one pole and to the top of the other. A heavy weight is hung on the rope and released, and it slides along the rope until it comes to rest at the lowest point it can reach. At what height above the ground does the weight hang then?
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Serbian Republic Competition (Republicko takmicenje) 1996, high school grade I, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source