Problems
Recall that a line is tangent to a circle if they have only one point
of intersection, a circle is called inscribed in a polygon if it is
tangent to every side as a segment of that polygon.
In the triangle \(EFG\) the line \(EH\) is the median. Two circles with
centres \(A\) and \(C\) are inscribed into triangles \(EFH\) and \(EGH\) respectively, they are tangent to the
median \(EH\) at the points \(B\) and \(D\). Find the length of \(BD\) if \(EF-EG=2\).
Draw how Robinson Crusoe should use pegs, ropes, and sliding rings to tie his goat in order for the goat to graze grass in the shape of a square.
Draw how Robinson Crusoe should put pegs and ropes to tie his goat in order for the goat to graze grass in the shape of a parallelogram.
Draw how Robinson Crusoe should put pegs and ropes to tie his goat in order for the goat to graze grass in an area of the following shape:
Draw how Robinson Crusoe should put pegs and ropes to tie his goat in order for the goat to graze grass in the shape of a given triangle.
Draw how Robinson Crusoe should arrange pegs and ropes so that his goat grazes in the shape of a hexagon. The hexagon doesn’t need to be regular.
Robinson Crusoe’s goat is tied to a single peg with one rope. Draw how Robinson should arrange pegs, ropes, a sliding ring, and a wolf so that the goat grazes in the shape of a half-circle.
Un día, Robinson encontró un lobo en la isla. Se lo llevó consigo y lo ató con una cuerda a una estaca. Robinson observó que la cabra no pastaba en ningún lugar al que pudiera llegar el lobo. ¿Cómo podría Robinson colocar a los dos animales con estacas y cuerdas para que la cabra solo pueda pastar en una región con forma de luna menguante? (ver la figura de abajo)
Draw how Robinson Crusoe should arrange pegs, ropes, and a wolf so that the goat grazes grass in the shape of a half-ring.
