Problems

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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) \(\sqrt {ab}\).

Construct a triangle with the side \(c\), median to side \(a\), \(m_a\), and median to side \(b\), \(m_b\).

Inside an angle two points, \(A\) and \(B\), are given. Construct a circle which passes through these points and cuts the sides of the angle into equal segments.