Construction of a Triangle

Geometry Level 3

Is it possible to construct a triangle if the following measures are given:

  • radius of incircle
  • radius of circumcircle
  • radius of one of the excircles
No Yes

Andreas Wendler by Andreas Wendler , 63, Germany

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Yuriy Kazakov
Mar 8, 2018

I use EulerTriangleFormula

R 2 − d 2 = 2 R r R^2 - d^2 = 2Rr and ( R + r o u t ) 2 = d o u t 2 + r o u t 2 (R+r_{out})^2=d^2_{out} + r_{out}^2

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Andreas Wendler
Nov 24, 2016

Write down the relations for the 3 radii respecting Heron's formula for triangle's area to get a non-linear equations' system for the lengths. If no mismatches (e.g. radius of incircle > radius of circumference) occur one will get at least one solution.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...