MathDB

12

Part of 2015 Hanoi Open Mathematics Competitions

Problems(2)

integer altitudes in triangle, 3,7 and d (2015 HOMC Junior Q12)

Source:

7/19/2019
Give a triangle ABCABC with heights ha=3h_a = 3 cm, hb=7h_b = 7 cm and hc=dh_c = d cm, where dd is an integer. Determine dd.
altitudesIntegergeometry
perpendiculars wanted, isosceles related (2015 HOMC Senior Q12)

Source:

7/19/2019
Give an isosceles triangle ABCABC at AA. Draw ray CxCx being perpendicular to CA,BECA, BE perpendicular to CxCx (E∈CxE \in Cx).Let MM be the midpoint of BEBE, and DD be the intersection point of AMAM and CxCx. Prove that BD⊥BCBD \perp BC.
geometryperpendicularisosceles