Construct Triangle by Angle, Altitude and Median

Construct $\Delta ABC,$ given $m_b,$ $h_a,$ and angle at $A.$

Construct Triangle by Angle, Altitude and Median - problem

Step 1: On a segment $AM_b$ of the given length $m_b$ construct circle $\kappa$ in which $AM_b$ sub tends the given angle at $A.$

Construct Triangle by Angle, Altitude and Median - construction

Step 2: Draw circle $C(M_b,h_a/2)$ centered at $M_b$ with radius $h_a/2.$

Step 3: Draw tangent from $B$ to $C(M_b,h_a/2)$ away from $\kappa.$

Step 4: Draw a line parallel to the latter at distance $h_a.$ Obtain $A$ at the intersection with $\kappa.$

Step 5: Draw $AM_b$ to find $C.$

There may be $0, 1,$ or $2$ solutions:

Construct Triangle by Angle, Altitude and Median - two solutions

The construction is due to Prof. Dr. René Sperb.

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