MathDB

2

Part of 2021 Stanford Mathematics Tournament

Problems(2)

SMT 2021 Geometry #2

Source:

8/9/2023
Let ABCDABCD be a trapezoid with bases AB=50AB = 50 and CD=125CD = 125, and legs AD=45AD = 45 and BC=60BC = 60. Find the area of the intersection between the circle centered at BB with radius BDBD and the circle centered at DD with radius BDBD. Express your answer as a common fraction in simplest radical form and in terms of π\pi.
geometry
SMT 2021 Geometry Tiebreaker #2

Source:

8/9/2023
If two points are picked randomly on the perimeter of a square, what is the probability that the distance between those points is less than the side length of the square?
geometry