Triangle from Median, Altitude and Circumradius

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

Triangle from Median, altitude and Circumradius - problem

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.


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