how to find the diameter using the a length across a circle

Question

I have to find the diameter of a pond in a question and i know only that a log that is across it is 16 ft long and the distance from that log perpendicular to the side of the circle measures 4ft. like this, roughly

                                                           _____

                                                       /      |<4ft    \

                                                   /  _____|_____   \

                                                          ^

                                                   \      16ft .           /

                                                       \                 /

                                                             ____

Answer 1

Hey!  Pretty cool pic!

This drawing is actually very helpful.

 

Now, extend the 4-ft line until it intersects the circle at the other side.  Let x be the length of the extension.  This forms two cords of a circle; one is 8 ft (4+4) and the other is (4+x) ft.  We will find the length (4+x), which is the diameter of the circle [you may want to verify that a line segment that is perpendicular to a cord and bisects it, goes through the center of the circle and forms the diameter of the circle).

 

This is where it gets super interesting –

The Intersecting Cords Theorem:  If two chords intersect inside a circle then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

  That means that –

        4x = 8*8

          x = 16

  diameter = (x+4) = 20 ft