Proposition 9

Construction

To bisect a given angle.

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Construction Steps

Let ∠BAC be the given angle.

Take a point D on AB , then find a point E on AC  such that ￜAD ￜ = ￜAE ￜ. Join DE .

Construct an equilateral triangle △EFD with base DE  and with vertex F falling on the opposite side of DE  from A. Join AF . ∠BAC has been bisected by AF .

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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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