MathDB

3

Part of 2014 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2014 Grade 6 Problem 3

Source:

10/3/2018
Let ABCABC be a right angled triangle. Prove that angle bisector of right angle is simultaneously an angle bisector of angle between median and altitude to hypotenuse.
geometryangle bisector
Junior Regional Olympiad - FBH 2014 Grade 7 Problem 3

Source:

10/3/2018
Let ABCDABCD be a trapezoid with base sides ABAB and CDCD and let AB=aAB=a, BC=bBC=b, CD=cCD=c, DA=dDA=d, AC=mAC=m and BD=nBD=n. We know that m2+n2=(a+c)2m^2+n^2=(a+c)^2 a)a) Prove that lines ACAC and BDBD are perpendicular b)b) Prove that ac<bdac<bd
geometrytrapezoid
Junior Regional Olympiad - FBH 2014 Grade 8 Problem 3

Source:

10/3/2018
If BKBK is an angle bisector of ∠ABC\angle ABC in triangle ABCABC. Find angles of triangle ABCABC if BK=KC=2AKBK=KC=2AK
geometryangle bisector