Problem 630: Clawson Point: Orthic Triangle, Extangents Triangle, Homothecy

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Level: High School, SAT Prep, College geometry

Archimedes' Arbelos and Square

Dynamic Geometry Software. Step-by-Step construction, Manipulation, and animation
In the figure, a circle D is inscribed in the arbelos ABC (AB, BC and AC are semicircles), prove that ELBK is a square.



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gogeometry.com/geometry/archimedes_arbelo_circle_square.htm

Elearn Geometry Problem 164

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Parallelogram, Trapezoid, Diagonal, Triangles, Areas. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 160

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Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 155

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Euler's Theorem: Distance from the Incenter to the Circumcenter. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 154

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Triangle, Inradius, Circumradius, Chord. Level: High School, SAT Prep, College geometry

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Menelaus' Theorem Proof

Proposition
Let ABC be a triangle and MEN a line that transverse (crosses) the lines AB, BC, and AC respectively. Prove that (AM.BE.CN)/(MB.EC.NA)=-1. The converse also holds.



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Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 139

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Triangle Area, Orthic Triangle, Semiperimeter, Circumradius. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 138 Nagel's Theorem

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Nagel's Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 137

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Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 136

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Orthic Triangle, Altitudes, Orthocenter, Incenter, Perpendicular, Concyclic Points. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 135

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Orthic Triangle, Altitudes, Perpendicular, Parallel. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 134

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Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter. Level: High School, SAT Prep, College geometry

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Interactive Simson Line

Proposition
Given a triangle ABC and P a point on its circumcircle, as shown. Prove that the feet D, E, and F of the perpendiculars drawn from P to the sides (or their extensions) are collinear. The line DEF is called the Simson line.



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Triangle, Circumcircle, Perpendiculars, Collinear feet points. Level: High School, SAT Prep, College geometry

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Dynamic Geometry: Triangle

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Triangle: Incircle, Perpendicular, Angle Bisector. Level: High School, SAT Prep, College geometry

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Elearn Geometry Problem 51

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Fagnano's Triangle Problem. Level: High School, SAT Prep, College geometry

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