Circle Tangent to Two Given Lines

Here is another problem that comes from the field of surveying. A park is being laid out with two one-mile access roads than run from a common point to each side of a circular field. At the points of tangency to the circle, the roads go around the circular field until they meet, completing a closed loop from the gate, along one road, around a part of the circular field from one tangent point to the other, and then back out the other road to the gate. The total length of the road is three miles -- one mile along each straight access road and one mile around the arc of the circle between the two tangent points. They want to know the radius of the circle.

Does the Problem provide enough information to solve it?



Numerical estimation and approximation?


Geometry constructions?







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