Omni-MATH / Let △ABC be an equilateral triangle of side length 1. Let D,E,F be points on BC,AC,AB respectively, such that (DE)/(20)=(EF)/(22)=(FD)/(38). Let X,Y,Z be on lines BC,CA,AB respecti…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Let △ABC be an equilateral triangle of side length 1. Let D,E,F be points on BC,AC,AB respectively, such that (DE)/(20)=(EF)/(22)=(FD)/(38). Let X,Y,Z be on lines BC,CA,AB respectively, such that XY⊥DE,YZ⊥EF,ZX⊥FD. Find all possible values of (1)/([DEF])+(1)/([XYZ]).

Let $\triangle ABC$ be an equilateral triangle of side length 1. Let $D,E,F$ be points on $BC,AC,AB$ respectively, such that $\frac{DE}{20} = \frac{EF}{22} = \frac{FD}{38}$. Let $X,Y,Z$ be on lines $BC,CA,AB$ respectively, such that $XY\perp DE, YZ\perp EF, ZX\perp FD$. Find all possible values of $\frac{1}{[DEF]} + \frac{1}{[XYZ]}$.

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

task_id

4d8e7fa2-cb02-56ee-b6d8-2c4fbb4e8383

task_key

test--4d8e7fa2-cb02-56ee-b6d8-2c4fbb4e8383

task_revision_id

3

config / split

/ test

Official source

initial import