A surveyor places a metre stick against the base of a large circular underground pipe and finds that the midpoint of the stick is 8 cm from the pipe wall.
Use this information to find the inside diameter of the pipe.
Using the Pythagorean Theorem, r2 = (r 8)2 + 502 = r2 16r + 64 + 2500
16r = 2564 r = 160.25
So the internal diameter is 320.5 cm.
What if the stick was 10 cm from the wall?
Can you generalise for any distance x?