Subject: GEOMETRIC PROBLEM
Date: Sun, 8 Nov 1998 14:29:38 +0200

I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler.

Thank you,
Victor

Hi Victor

The problem is easy to start: A bisectrix consists of 3 hyperbolas that come together in 3 cusps. Pascal's theorem enables one to find the tangents at those three cusps so, essentially, we are given three fixed lines passing through the centroid of the desired triangle. In other words, the problem reduces to,
 Given the 3 lines l, m, n through a point G, and given two numbers a and b, construct a triangle whose centroid is G, whose medians lie on l, m, and n, and two of the sides have length a and b.
If you let C' be any point of n, then the midpoint of the opposite side is found using the fact the G cuts the median in the ratio 2:1. Use that point to construct the triangle A'B'C' similar to the desired triangle, and get ABC by dilatation.

Perhaps this is enough to get started.

Cheers
Chris

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