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. Using only straightedge and compass construct a segment of length: a) \(ab/c\); b) \(\sqrt {ab}\).
In a triangle, the lengths of two of the sides are 3.14 and 0.67. Find the length of the third side if it is known that it is an integer.
Prove that, with central symmetry, a circle transforms into a circle.
The opposite sides of a convex hexagon are pairwise equal and parallel. Prove that it has a centre of symmetry.
The symmetry axis of the polygon intersects its sides at points \(A\) and \(B\). Prove that the point \(A\) is either the vertex of the polygon or the middle of the side perpendicular to the axis of symmetry.
Prove that a circle transforms into a circle when it is rotated.