import R2Graph

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-- Compute a circle inscribed in a triangle
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incircle :: Triangle -> Circle
incircle t =
    let
        n1 = normalize ((vertex1 t) `subtractPoints` (vertex0 t))
        n2 = normalize ((vertex2 t) `subtractPoints` (vertex0 t))
        b0 = n1 `addVectors` n2

        n3 = normalize ((vertex2 t) `subtractPoints` (vertex1 t))
        n4 = n1 `multiplyVector` (-1)
        b1 = n3 `addVectors` n4

        bis0 = Line (vertex0 t) b0
        bis1 = Line (vertex1 t) b1

        (Just c) = intersectLines bis0 bis1
        r = c `distanceToLine` (Line (vertex0 t) n1)
    in
        Circle c r