MathDB

2021.9.5

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

AB=BQ wanted, AB\\ PC , PM_|_ BM, median (2021 Kyiv City MO 9.5)

Source:

2/15/2021
Let BMBM be the median of the triangle ABCABC, in which AB>BCAB> BC. Point PP is chosen so that AB∥PCAB \parallel PC andPM⊥BM PM \perp BM. The point QQ is chosen on the line BPBP so that ∠AQC=90o\angle AQC = 90^o, and the points BB and QQ lie on opposite sides of the line ACAC. Prove that AB=BQAB = BQ.
(Mikhail Standenko)
geometryequal segmentsmedian