MathDB

4

Part of 1999 May Olympiad

Problems(2)

proof of angle bisector within an equilateral triangle

Source: May Olympiad (Olimpiada de Mayo) 1999 L2

9/12/2018
Let ABCABC be an equilateral triangle. MM is the midpoint of segment ABAB and NN is the midpoint of segment BCBC. Let PP be the point outside ABCABC such that the triangle ACPACP is isosceles and right in PP. PMPM and ANAN are cut in II. Prove that CICI is the bisector of the angle MCAMCA .
geometryangle bisectorEquilateral Triangle
10 triangles and 10 trapezoids , to aseemble a square

Source: V May Olympiad (Olimpiada de Mayo) 1999 L1 P4

9/17/2022
Ten square cardboards of 33 centimeters on a side are cut by a line, as indicated in the figure. After the cuts, there are 2020 pieces: 1010 triangles and 1010 trapezoids. Assemble a square that uses all 2020 pieces without overlaps or gaps. https://cdn.artofproblemsolving.com/attachments/7/9/ec2242cca617305b02eef7a5409e6a6b482d66.gif
combinatoricscombinatorial geometry