Proposition 23

Construction

On a given line segment and at a point on it to construct an angle equal to a given angle.

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Construction Steps

Let K be the given point on the given line segment AB  and let ∠ECD be the given angle.

On KB , pick a point F such that ￜKF ￜ < ￜCD ￜ.

On CD , find a point P such that ￜCP ￜ = ￜKF ￜ.

Take a point Q on CE , and join QP .

Find a point G to satisfy ￜKG ￜ = ￜCQ ￜ and ￜGF ￜ = ￜQP ￜ. At the given point K on the given line AB , the angle ∠GKF has been constructed equal to the given angle ∠ECD.

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Computable version

In[1]:=

GeometricScene[{{A.,B.,C.,O.,D.,E.,F.,G.},{}},​​{GeometricStep[{CircleThrough[{A.,B.,C.},O.],Line[{A.,O.,C.}],Line[{D.,E.}],EuclideanDistance[D.,E.]≤EuclideanDistance[A.,C.]}],​​GeometricStep[{F.∈Line[{A.,C.}],EuclideanDistance[A.,F.]EuclideanDistance[D.,E.]}],​​GeometricStep[{GeometricAssertion[{CircleThrough[{F.},A.],CircleThrough[{A.,B.,C.},O.]},{"Concurrent",G.}]}],​​GeometricStep[{Line[{A.,G.}]}]},​​{EuclideanDistance[A.,G.]EuclideanDistance[D.,E.]}​​]//RandomInstance

Out[]=

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Additional instances

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Dependency graphs