Planning road construction. Two towns A and B are located 8 and 5 miles, respectively, fro...

Planning road construction. Two towns A and B are located 8 and 5 miles, respectively, from a long, straight highway. The points C and D on the highway closest to the two towns are 18 miles apart. (Remember that the shortest distance from a point to a line is the length of the perpendicular segment from the point to the line.) Where should point E be located on the highway so that the sum of the lengths of the roads from A to E and E to B is 23 miles? (See the accompanying figure.)

[Hint: 205x2 – 4392x + 18972 = (x – 6) (205x – 3162).]