A circular playground has 2 parellel roads running through it. Their lengths are 112m and 50m. The perpendicular distance between these roads is 92m.

Find the diameter of the playground.

Set up Cartesian coordinates such that the center of the circle is at (0, 0), Points A and B (the ends of the 50m roadway) are at (-25, y') and (25, y') and points C and D (the ends of the 112m roadway) are at (-56, y' - 92) and (56, y' - 92).

Points B (25, y') and D (56, y' - 92) are both r meters away from (0, 0), so we get the equations:

r² = 625 + (y')²

r² = 3136 + (y' - 92)² = 3136 + (y')² - 184(y') + 8464

It's getting a little late to work out the fine details with a clear mind, so I'll finish in the morning, but basically, you just solve for r and then D (the diameter of the playground ) is 2r

Posted by TomM on 2002-08-01 18:05:16