MathDB

3

Part of 2019 ASDAN Math Tournament

Problems(3)

2019 Geometry # 3

Source:

9/10/2023
Consider an equilateral triangle △ABC\vartriangle ABC with side length 11. Let DD and EE lie on segments ABAB and ACAC respectively such that ∠ADE=30o\angle ADE = 30^o and DEDE is tangent to the incircle of △ABC\vartriangle ABC. Compute the perimeter of △ADE\vartriangle ADE.
geometry2019
2019 Discrete Tiebreaker #3

Source:

10/5/2022
55 monkeys, 55 snakes, and 55 tigers are standing in line at the local grocery store, with animals of the same species being indistinguishable. A monkey stands at the front of the line and a tiger stands at the end of the line. Unfortunately, monkeys and tigers are sworn enemies, so monkeys and tigers cannot stand in adjacent places in line. Compute the number of possible arrangements of the line.
2019Discrete Math Tiebreaker
2019 Geometry Tiebreaker #3

Source:

9/10/2023
Consider a triangle △ABC\vartriangle ABC with BC=10BC = 10. An excircle is a circle that is tangent to one side of the triangle as well as the extensions of the other two sides; suppose that the excircle opposite vertex BB has center I2I_2 and exradius r2=11r_2 = 11, and suppose that the excircle opposite vertex CC has center I3I_3 and exradius r3=13r_3 = 13. Compute I2I3I_2I_3.
Geometry Tiebreaker2019