Diameter of a circle using 3 nonlinear points

Question

I am trying to find the diameter of a circle using 3 points on its circumference. 2 of the points are 5 feet from eachother while the third point is centered between the other 2. The ceter point is 1 foot from a line drawn between the other 2 points.

Answer 1

Hint: If two chords $AB$ and $CD$ of a circle intersect at $P$, then $AP\cdot PB=CP\cdot PD$. Draw the diameter joining the red and green lines in your diagram. So, $AP=PB=\dfrac{5}{2}$ and $CP=1$, and hence $DP=\dfrac{25}{4}$. Now you can compute the diameter.

Answer 2

Alternatively you may use of following property: "The circumcenter of a triangle can be found as the intersection of any two of the three perpendicular bisectors."

Adjust your figure accordingly and search for similar triangles.

Answer 3

So you have an arc whose chord is l=5 feet long and the sagitta is s=1 fooot.
See Wikipedia article http://en.wikipedia.org/wiki/Sagitta_(geometry)