MathDB

2

Part of 2024 Caucasus Mathematical Olympiad

Problems(2)

Easy perpendicularity

Source: Caucasus MO 2024, Juniors P2

3/15/2024
The rhombuses ABDKABDK and CBELCBEL are arranged so that BB lies on the segment ACAC and EE lies on the segment BDBD. Point MM is the midpoint of KLKL. Prove that ∠DME=90∘\angle DME=90^{\circ}.
geometry
Easy conditional geometry

Source: Caucasus MO 2024, Seniors P2

3/15/2024
In an acute-angled triangle ABCABC let BLBL be the bisector, and let BKBK be the altitude. Let the lines BLBL and BKBK meet the circumcircle of ABCABC again at WW and TT, respectively. Given that BC=BWBC = BW, prove that TL⊥BCTL \perp BC.
geometry