# Triangle from Median, Altitude and Circumradius

Construct $\Delta ABC,$ given the median $m_a,$ altitude $h_a,$ and Circumradius $R.$

### Construction

The construction is straightforward: start with $\Delta AM_{a}H_{a};$ then find the circumcenter $O$ at the intersection of the perpendicular to $M_{a}H_{a}$ at $M_{a}$ and the circle $C(A,R),$ with center $A$ and radius $R.$ This defines the circumcircle $(O)$ and the tangents from $A$ that give the vertices $B$ and $C.$

### Acknowledgment

The construction was communicated to me by Prof. Dr. René Sperb.

|Contact| |Front page| |Contents| |Up|

Copyright © 1996-2018 Alexander Bogomolny65240371 |