MathDB

1

Part of 2021 New Zealand MO

Problems(2)

school offers three subjects: Mathematics, Art and Science

Source: New Zealand MO 2021 Round 1 p1

9/20/2021
A school offers three subjects: Mathematics, Art and Science. At least 80%80\% of students study both Mathematics and Art. At least 80%80\% of students study both Mathematics and Science. Prove that at least 80%80\% of students who study both Art and Science, also study Mathematics.
combinatorics
BD=? AB + BC = 2021, AD = CD, <ABC = <CDA = 90^o

Source: New Zealand MO 2021 Round 2 p1 NZMO

10/6/2021
Let ABCDABCD be a convex quadrilateral such that AB+BC=2021AB + BC = 2021 and AD=CDAD = CD. We are also given that ∠ABC=∠CDA=90o\angle ABC = \angle CDA = 90^o. Determine the length of the diagonal BDBD.
geometryright angleequal segments