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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.

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# B Understanding A Middle Ordinate In Terms Of Geometry

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