Waste less time on Facebook — follow Brilliant.
×

Help on this Geometry Problem!

Prove that in \(\triangle ABC\), circle \(ABC\) is the nine-point circle of the extracentral triangle of \(ABC\), that is, the triangle whose vertices comprise of the excenters.

You are free to share your proof below in the comments section.

Note by Alan Yan
2 years, 2 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

\(\triangle ABC\) is orthic triangle of the triangle whose vertices are ex-centers. To reverse the scenario, if we look at the orthic triangle of any given acute triangle, its angle bisectors are altitudes and sides of the reference triangle. This means that circumcirle of the orthic triangle is nine point circle of the reference triangle.

Maria Kozlowska - 2 years, 2 months ago

Log in to reply

Wait how do you know that \(\triangle ABC\) is the orthic triangle?

Alan Yan - 2 years, 2 months ago

Log in to reply

Carefully read the second statement and make a good drawing. You can also check this website: orthic triangle

Maria Kozlowska - 2 years, 2 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...