## Wednesday, November 16, 2011

### Problems in Geometry Series 1

I have uploaded a new lecture to http://www.unizor.com/ with the following geometrical problems.

1. Construct a triangle by two sides and a median to the third side.

2. Construct a quadrangle by all four sides and a median segment connecting midpoints of opposite sides.
Hint: use parallel shift.

3. Construct a trapezoid by one of its interior angles, two diagonals and a median (segment between midpoints of two non-parallel sides).
Hint: use parallel shift.

4. Construct a quadrangle by three sides and two interior angles adjacent to one of known sides.
Hint: use parallel shift.

5. Construct a trapezoid by its two bases and two legs.
Hint: use parallel shift.

6. Construct a quadrangle by its four sides, provided one diagonal bisects one angle it is connected to.
Hint: use symmetry relative to an axis.

7. A billiard table has a rectangular shape. There are two balls on it in some position. Determine direction of the movement of one ball in such a way, that, reflecting from all four sides, it will hit the second ball.
Hint: use symmetry relative to table borders on each side.