Proposition 11

Construction

From a given point in a given line segment to draw a straight line perpendicular to the given line.

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Construction Steps

Let AB  be the given line segment and let C be the given point on it.

Take a point D on AC , and find a point E on BC  such that ￜCE ￜ = ￜCD ￜ.

Construct an equilateral triangle △DFE with DE  as the base. Join CF . The line CF  is perpendicular to the given line segment AB  at the given point C.

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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