Find the locus of the midpoints of the segments, the ends of which are found on two given parallel lines.
Find the locus of the points \(X\) such that the tangents drawn from \(X\) to a given circle have a given length.
The point \(A\) is fixed on a circle. Find the locus of the point \(X\) which divides the chords that end at point \(A\) in a \(1:2\) ratio, starting from the point \(A\).
Let \(O\) be the center of the rectangle \(ABCD\). Find the geometric points of \(M\) for which \(AM \geq OM, BM \geq OM\), \(CM \geq OM\), and \(DM \geq OM\).
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 the triangle ABC by the medians \(m_a, m_b\) and \(m_c\).
Construct a triangle with the side \(c\), median to side \(a\), \(m_a\), and median to side \(b\), \(m_b\).
Construct a triangle with the side \(a\), the side \(b\) and height to side \(a\), \(h_a\).