Problems

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 \(m_c\).

Solve the equations \(x^2 = 14 + y^2\) in integers.

Cut a square into two equal:
1. Triangles.
2. Pentagons
3. Hexagons.

Cut the following figure into two equal parts.

Suppose that a rectangle can be divided into \(13\) equal smaller squares. What could be the side lengths of this rectangle?

Cut a square into \(3\) parts which you can use to construct a triangle with angles less than \(90^{\circ}\) and three different sides.

Can you find a quadrilateral (i.e: a shape with four sides) that can be divided into \(6\) shapes (not necessarily congruent) by using only two straight cuts?

Cut the following shape into four equal figures.