MathDB

G5

Part of 2018 JBMO Shortlist

Problems(1)

strange area condition given (GCE)=1/2 (a^3/b+ab) inside a rectangle

Source: JBMO Shortlist 2018 G5

7/22/2019
Given a rectangle ABCDABCD such that AB=b>2a=BCAB = b > 2a = BC, let EE be the midpoint of ADAD. On a line parallel to ABAB through point EE, a point GG is chosen such that the area of GCEGCE is (GCE)=12(a3b+ab)(GCE)= \frac12 \left(\frac{a^3}{b}+ab\right) Point HH is the foot of the perpendicular from EE to GDGD and a point II is taken on the diagonal ACAC such that the triangles ACEACE and AEIAEI are similar. The lines BHBH and IEIE intersect at KK and the lines CACA and EHEH intersect at JJ. Prove that KJ⊥ABKJ \perp AB.
geometryrectanglearea of a trianglesimilar trianglesperpendicular