Tangent on an arc between two angles. Unknown variables.

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Please see the link below for an image of the geometry I will be referencing. I am trying to find the radius (length F) of the tangent arc, given the assumption that lines D and C are always vertical and a fixed length, and angle c is always split equally as shown.

As you change the angle c, the tangent circle will change in radius, and this will change all other unknown variables accordingly.

This is a fully defined problem when considering D and C to be vertical. There can be no other changes to the geomtery without changing fixed variables, thus it should be able to be calculated.

I've been thinking about this problem for weeks. I've tried following another post i found on here, but i'm not sure how to relate it to my specific problem: arc tangent to two lines and through a point

Look forward to hearing peoples suggestions.

Thanks

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