MathDB

13

Part of 2021 Durer Math Competition Finals

Problems(2)

trapezoid ABCD, AB = 70, AD = 32 , BC = 49, <ABC = 3 <ADC

Source: 2021 Dürer Math Competition Finals Day2 E13 https://artofproblemsolving.com/community/c2749870

1/8/2022
The trapezoid ABCDABCD satisfies AB∥CDAB \parallel CD, AB=70AB = 70, AD=32AD = 32 and BC=49BC = 49. We also know that ∠ABC=3∠ADC\angle ABC = 3 \angle ADC. How long is the base CDCD?
geometrytrapezoidequal angles
a table tennis competition

Source: 2021 Dürer Math Competition Finals Day2 E+13 https://artofproblemsolving.com/community/c2749870_

1/9/2022
At a table tennis competition, every pair of players played each other exactly once. Every boy beat thrice as many boys as girls, and every girl was beaten by twice as many girls as boys. How many competitors were there, if we know that there were 1010 more boys than girls? There are no draws in table tennis, every match was won by one of the two players.
combinatorics