Intersections of BisectorsDate: 9/6/95 at 14:0:50 From: "$info" Subject: analytic geometry Explain how to get the incenter and the circumcenter of a triangle. Also, how to get the orthocenter of a triangle. Date: 9/13/95 at 12:56:21 From: Doctor Steve Subject: Re: analytic geometry There are a few key lines in any triangle that are worth exploring because they generate so many interesting relations. Try constructing the angle bisectors and then exploring their intersection(s?) in relation to the other elements of the triangle. Try the same with the perpendicular bisectors, and then again with the altitudes, and then again with the medians. I have written out some answers below where it says "SPOILER." Try exploring first before reading those. -Doctor Steve, The Geometry Forum *******SPOILER********* Angle bisectors intersect at the incenter Perpendicular bisectors at the circumcenter Altitudes at the orthocenter Medians at the centroid Extra credit question: what use is the centroid? |
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