MathDB

4

Part of 2016 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2016 Grade 6 Problem 4

Source:

9/29/2018
Let CC and DD be points inside angle ∠AOB\angle AOB such that 5∠COD=4∠AOC5\angle COD = 4\angle AOC and 3∠COD=2∠DOB3\angle COD = 2\angle DOB. If ∠AOB=105∘\angle AOB = 105^{\circ}, find ∠COD\angle COD
geometryAngle Chasing
Junior Regional Olympiad - FBH 2016 Grade 7 Problem 4

Source:

9/29/2018
In right angled triangle ABCABC point DD is midpoint of hypotenuse, and EE and FF are points on shorter sides ACAC and BCBC, respectively, such that DE⊥DFDE \perp DF. Prove that EF2=AE2+BF2EF^2=AE^2+BF^2
geometry
Junior Regional Olympiad - FBH 2016 Grade 8 Problem 4

Source:

9/29/2018
In set of positive integers solve the equation x3+x2y+xy2+y3=8(x2+xy+y2+1)x^3+x^2y+xy^2+y^3=8(x^2+xy+y^2+1)
number theoryequations