MathDB

2

Part of 2019 Stanford Mathematics Tournament

Problems(2)

SMT 2019 Geometry #2 cat and mouse

Source:

8/8/2023
A cat and mouse live on a house mapped out by the points (−1,0)(-1, 0), (−1,2)(-1, 2), (0,3)(0, 3), (1,2)(1, 2), (1,0)(1, 0). The cat starts at the top of the house (point (0,3)(0, 3)) and the mouse starts at the origin (0, 0). Both start running clockwise around the house at the same time. If the cat runs at 1212 units a minute and the mouse at 9 units a minute, how many laps around the house will the cat run before it catches the mouse?
geometryanalytic geometry
SMT 2019 Geometry Tiebreaker #2

Source:

8/8/2023
Let ABCDABCD be a rectangle with AB=8AB = 8 and BC=6BC = 6. Point EE is outside of the rectangle such that CE=DECE = DE. Point DD is reflected over line AEAE so that its image, D′D' , lies on the interior of the rectangle. Point D′D' is then reflected over diagonal ACAC, and its image lies on side ABAB. What is the length of DEDE?
geometry