Circumcircle of a Triangle in a Cube

Topic:Cube

Randomly choose a lattice point (not an edge point) on each of three adjacent faces on a cube. There is a unique circle through those three points. What is the area of the typical circle constructed in this way?

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Congruent Figures
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Segment Addition Postulate (Mild Questions)
Rovnoběžnost rovin
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Mackenzie's Porabola
Parallel method
Parabola Shifts
Paraboloide
Tangential Plane

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Sphere
Trigonometric Functions
Area
Similar Triangles
Ratios