Baltic Way 2019 · Problem 13

Geometry

Let $ABCDEF$ be a convex hexagon in which $AB=AF$ , $BC=CD$ , $DE=EF$ and $\angle ABC=\angle EFA=90^\circ$ . Prove that $AD\perp CE$ .

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Review

Topics

Cyclic geometry · Circles and tangency

Solutions

Solution

Consider circle $\omega$ with centre $A$ and radius $AB$ . Note that $BC$ and $EF$ are tangent to $\omega$ and so from the problem condition, the line $CE$ is a radical axis of $\omega$ and $D$ . Therefore $CE \perp AD$ .

Contest context

Results from Baltic Way 2019

11 teams

Mean score: 3.2 / 5
Scores of 4 or 5: 7 / 11
Estonia: 5 / 5

Score distribution

All team scores

Team	Score
St. Petersburg	5 / 5
Poland	5 / 5
Estonia	5 / 5
Lithuania	0 / 5
Germany	0 / 5
Norway	5 / 5
Finland	5 / 5
Denmark	5 / 5
Sweden	5 / 5
Latvia	0 / 5
Iceland	0 / 5

Elsewhere

AoPS · Baltic Way 2019
Official results