October 1st and Geometry

Geometry Level 1

Two towers, BC and ED, are lengths 1 and 10 respectively.

The line CD connects BC and ED such that Angle BCD = Angle EDC = 90º.

There is a point F, on the line CD, such that Angle BFE is also 90º.

The shortest possible length of CD can be expressed as √m, where m is a positive integer. Find m.

Note: The diagram below shown is not drawn to scale.

1 100 10 101 11

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