Problems

Construct the triangle $ABC$ along the side $a$, the height $h_a$ and the angle $A$.

Construct a right-angled triangle along the leg and the hypotenuse.

Construct a circle with a given centre, tangent to a given circle.

Construct a straight line passing through a given point and tangent to a given circle.

Three segments whose lengths are equal to $a,b$ and $c$ are given. Construct a segment of length: a) $ab/c$; b) $\sqrt{ab}$.

Prove that $S_{ABC}\le AB\times BC/2$.