MathDB

5

Part of 2015 Saint Petersburg Mathematical Olympiad

Problems(2)

Squares, rectangles and areas

Source: Saints Petersburg Olympiad 2015

7/9/2017
Square with side 100 was cut by 99 horizontal and 99 vertical lines into 10000 rectangles (not necessarily with integer sides). How many rectangles in this square with area not exceeding 1 at least can be?
rectanglecombinatorics
Pentagon angles

Source: St Petersburg Olympiad 2015, Grade 10, P5

10/17/2017
ABCDEABCDE is convex pentagon. ∠BCA=∠BEA=∠BDA2,∠BDC=∠EDA\angle BCA=\angle BEA = \frac{\angle BDA}{2}, \angle BDC =\angle EDA. Prove, that ∠DEB=∠DAC\angle DEB=\angle DAC
geometry