Altitudes and Orthocentres

The Problem :

Using Cabri-Géomètrie, or Geometers’ SketchPad, construct a circle of convenient size and then a triangle whose vertices lie on the circumference of the circle. Find the meeting point of two altitudes of the triangle.

·         What is the locus of this point of intersection as one of the vertices moves around the circumference of the circle?

[Definition : an altitude is a perpendicular drawn from one vertex to the opposite edge]

·         Prove the result that you have found.

Prove that the three altitudes intersect at a single point (called the Orthocentre)

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Last modified: June 18, 2007