MathDB

7

Part of 2022 MMATHS

Problems(2)

2022 MMATHS Team Online p7 - 3 right angles and midpoint arc

Source:

10/1/2023
△ABC\vartriangle ABC satisfies AB=16AB = 16, BC=30BC = 30, and ∠ABC=90o\angle ABC = 90^o. On the circumcircle of △ABC\vartriangle ABC, let PP be the midpoint of arc ACAC not containing BB, and let XX and YY lie on lines ABAB and BCBC, respectively, with PX⊥ABPX \perp AB and PY⊥BCPY \perp BC. Find XY2XY^2.
geometryMMATHS
2022 MMATHS Individual p7 - percentages and dollars

Source:

10/1/2023
Katherine makes Benj play a game called 5050 Cent. Benj starts with $0.50\$0.50, and every century thereafter has a 50%50\% chance of doubling his money and a 50%50\% chance of having his money reset to $0.50\$0.50. What is the expected value of the amount of money Benj will have, in dollars, after 5050 centuries?
algebraMMATHS