Hello community I was hoping someone could help me with the following problem. I am trying to understand what a middle Ordinate is in terms of geometry (I know it has a versine along a chord). Given the diagram below:- The Blue line is an arc of some radius. AB & CB are both tangent to the arc and intersect at point B. AD is 90 Degrees to AB CB is 90 Degrees to CD My question is if i drew a line from D to B will that line intersect AC at exactly half its length i.e. at AC/2. If this is correct then will the length of line EF be its longest when line DB intersects AC at exactly half its length. I believe that line DB will Always intersect AC at half its distance because AD and CD are the same length making an isosceles triangle. I also believe that the line EF will be its longest when measured exactly half way along line AC but I cannot prove it. I was hoping someone could shed some light. Thank you all.