MathDB

1

Part of 2018 Bulgaria JBMO TST

Problems(2)

minimum of f(a, b) + f (a,-b) + f(-a, b) + f (-a, -b)

Source: Bulgaria JBMO TST 2018, Day 2, Problem 1

6/25/2018
For real numbers aa and bb, define f(a,b)=a2+b2+26a+86b+2018.f(a,b) = \sqrt{a^2+b^2+26a+86b+2018}. Find the smallest possible value of the expression f(a,b)+f(a,−b)+f(−a,b)+f(−a,−b).f(a, b) + f (a,-b) + f(-a, b) + f (-a, -b).
inequalities2018
Find the length of diagonal AC

Source: Bulgaria JBMO TST 2018, Day 1, Problem 1

6/25/2018
In the quadrilateral ABCDABCD, we have ∡BAD=100∘\measuredangle BAD = 100^{\circ}, ∡BCD=130∘\measuredangle BCD = 130^{\circ}, and AB=AD=1AB=AD=1 centimeter. Find the length of diagonal ACAC.
geometry