benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / In right triangle ABC, ∠B=90^(∘), and D and E lie on AC such that (BD)¯ is a median and (BE)¯ is an altitude. If BD=2⋅DE, compute (AB)/(EC). [asy] pair A,B,C,D,E; A=(0,0); C=(2,0);…

Problem

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

problem

In right triangle ABCABC, ∠B=90∘\angle B = 90^\circ, and DD and EE lie on ACAC such that BD¯\overline{BD} is a median and BE¯\overline{BE} is an altitude. If BD=2⋅DEBD=2\cdot DE, compute ABEC\frac{AB}{EC}. [asy] pair A,B,C,D,E; A=(0,0); C=(2,0); B=(1.5,sqrt(3)/2); D=(1,0); E=(1.5,0); draw(A--B--C--cycle); draw(B--D); draw(B--E); label("AA",A,SW); label("BB",B,N); label("CC",C,SE); label("DD",D,S); label("EE",E,S); draw(rightanglemark(B,E,D,2)); [/asy]
Plain-text mathematical notation (without MathML)
In right triangle ABC, ∠B=90^(∘), and D and E lie on AC such that (BD)¯ is a median and (BE)¯ is an altitude.  If BD=2⋅DE, compute (AB)/(EC). [asy]

pair A,B,C,D,E;

A=(0,0); C=(2,0); B=(1.5,sqrt(3)/2); D=(1,0); E=(1.5,0);

draw(A--B--C--cycle); draw(B--D); draw(B--E);

label("A",A,SW); label("B",B,N); label("C",C,SE); label("D",D,S); label("E",E,S);

draw(rightanglemark(B,E,D,2));

[/asy]
Original LaTeX notation
In right triangle $ABC$, $\angle B = 90^\circ$, and $D$ and $E$ lie on $AC$ such that $\overline{BD}$ is a median and $\overline{BE}$ is an altitude.  If $BD=2\cdot DE$, compute $\frac{AB}{EC}$. [asy]

pair A,B,C,D,E;

A=(0,0); C=(2,0); B=(1.5,sqrt(3)/2); D=(1,0); E=(1.5,0);

draw(A--B--C--cycle); draw(B--D); draw(B--E);

label("$A$",A,SW); label("$B$",B,N); label("$C$",C,SE); label("$D$",D,S); label("$E$",E,S);

draw(rightanglemark(B,E,D,2));

[/asy]

level

Level 5

type

Geometry

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. 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. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
94d3245b-5063-5382-815e-05d1a6551acf
task_key
geometry--test--94d3245b-5063-5382-815e-05d1a6551acf
task_revision_id
1
config / split
geometry / test

Official source

initial import