MathDB

5

Part of 2017 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2017 Grade 6 Problem 5

Source:

9/20/2018
Fathers childhood lasted for one sixth part of his life, and he married one 88th after that and he immediately left to army. When one 1212th of his life passed, father returned from the army and 55 years after he got a son. Son who lived for one half of fathers years, died 44 years before his father. How many years lived his father, and how many years he had when his son was born?
equation
Junior Regional Olympiad - FBH 2017 Grade 7 Problem 5

Source:

9/20/2018
Find all positive integers aa and bb such that number p=2+a3+bp=\frac{\sqrt{2}+\sqrt{a}}{\sqrt{3}+\sqrt{b}} is rational number
rationalsqaure roots
Junior Regional Olympiad - FBH 2017 Grade 8 Problem 5

Source:

9/20/2018
Points KK and LL are on side ABAB of triangle ABCABC such that KL=BCKL=BC and AK=LBAK=LB. Let MM be a midpoint of ACAC. Prove that ∠KML=90∘\angle KML = 90^{\circ}
geometrymidpointright angle