MathDB

3

Part of 2012 Junior Balkan Team Selection Tests - Moldova

Problems(2)

bisector inside equilateral triangle

Source:

8/9/2012
Let ABC ABC be an equilateral triangle, take line t t such that t∥BC t\parallel BC and t t passes through A A . Let point D D be on side AC AC , the bisector of angle ABD ABD intersects line t t in point E E . Prove that BD=CD+AE BD = CD + AE .
trigonometrygeometry
Isosceles triangle bisectors

Source:

8/9/2012
Let ABC ABC be an isosceles triangle with AC=BC AC=BC . Take points D D on side ACAC and EE on side BCBC and F F the intersection of bisectors of angles DEB DEB and ADEADE such that F F lies on side ABAB. Prove that FF is the midpoint of ABAB.
geometryangle bisectorperpendicular bisectorgeometry proposed