Understanding Ceva's Theorem Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Ratio of areas of similar triangles given SSHow to calculate Fermat point in a triangle most efficiently?Prove this is a rectangleThe formula for the area of two triangles determined by the diagonals of a trapezoidUSAMO 2005, Problem3 (Triangle Geometry)- Is my solution correct?Corresponding side in similar trianglesMake isosceles triangle with matchsticksCutting a Triangle Through Its CentroidSimilar triangles and cross section integrals.Postulate or Theorem: The areas of similar plane figures are proportional their linear dimensions squared?
The logistics of corpse disposal
51k Euros annually for a family of 4 in Berlin: Is it enough?
How does the particle を relate to the verb 行く in the structure「A を + B に行く」?
2001: A Space Odyssey's use of the song "Daisy Bell" (Bicycle Built for Two); life imitates art or vice-versa?
String `!23` is replaced with `docker` in command line
How do I keep my slimes from escaping their pens?
Storing hydrofluoric acid before the invention of plastics
Ring Automorphisms that fix 1.
What's the purpose of writing one's academic biography in the third person?
Why didn't this character "real die" when they blew their stack out in Altered Carbon?
Can a non-EU citizen traveling with me come with me through the EU passport line?
What is known about the Ubaid lizard-people figurines?
What is Arya's weapon design?
Why is my conclusion inconsistent with the van't Hoff equation?
How to call a function with default parameter through a pointer to function that is the return of another function?
Understanding Ceva's Theorem
Do I really need recursive chmod to restrict access to a folder?
3 doors, three guards, one stone
How to react to hostile behavior from a senior developer?
When were vectors invented?
Short Story with Cinderella as a Voo-doo Witch
What is a non-alternating simple group with big order, but relatively few conjugacy classes?
What would be the ideal power source for a cybernetic eye?
When do you get frequent flier miles - when you buy, or when you fly?
Understanding Ceva's Theorem
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Ratio of areas of similar triangles given SSHow to calculate Fermat point in a triangle most efficiently?Prove this is a rectangleThe formula for the area of two triangles determined by the diagonals of a trapezoidUSAMO 2005, Problem3 (Triangle Geometry)- Is my solution correct?Corresponding side in similar trianglesMake isosceles triangle with matchsticksCutting a Triangle Through Its CentroidSimilar triangles and cross section integrals.Postulate or Theorem: The areas of similar plane figures are proportional their linear dimensions squared?
$begingroup$
In Ceva's Theorem, I understand that $fracA_triangle PXBA_triangle PXC=fracBXCX=fracA_triangle BXAA_triangle CXA$.
I would like clarification in understanding the following step which states:
$fracA_triangle APBA_triangle APC=fracA_triangle AXB - A_triangle PXBA_triangle AXC-A_triangle PXC=fracBXCX$
How does the subtraction of the two areas make it so that the new triangles are still proportional to $fracBXCX$? (even though they do not share those sides!)
geometry proof-verification triangles
edited 2 hours ago
YuiTo Cheng
2,48341037
asked 2 hours ago
dragonkingdragonking
384
$endgroup$
add a comment |
$begingroup$
In Ceva's Theorem, I understand that $fracA_triangle PXBA_triangle PXC=fracBXCX=fracA_triangle BXAA_triangle CXA$.
I would like clarification in understanding the following step which states:
$fracA_triangle APBA_triangle APC=fracA_triangle AXB - A_triangle PXBA_triangle AXC-A_triangle PXC=fracBXCX$
How does the subtraction of the two areas make it so that the new triangles are still proportional to $fracBXCX$? (even though they do not share those sides!)
geometry proof-verification triangles
edited 2 hours ago
YuiTo Cheng
2,48341037
asked 2 hours ago
dragonkingdragonking
384
$endgroup$
add a comment |
$begingroup$
In Ceva's Theorem, I understand that $fracA_triangle PXBA_triangle PXC=fracBXCX=fracA_triangle BXAA_triangle CXA$.
I would like clarification in understanding the following step which states:
$fracA_triangle APBA_triangle APC=fracA_triangle AXB - A_triangle PXBA_triangle AXC-A_triangle PXC=fracBXCX$
How does the subtraction of the two areas make it so that the new triangles are still proportional to $fracBXCX$? (even though they do not share those sides!)
geometry proof-verification triangles
edited 2 hours ago
YuiTo Cheng
2,48341037
asked 2 hours ago
dragonkingdragonking
384
$endgroup$
In Ceva's Theorem, I understand that $fracA_triangle PXBA_triangle PXC=fracBXCX=fracA_triangle BXAA_triangle CXA$.
I would like clarification in understanding the following step which states:
$fracA_triangle APBA_triangle APC=fracA_triangle AXB - A_triangle PXBA_triangle AXC-A_triangle PXC=fracBXCX$
How does the subtraction of the two areas make it so that the new triangles are still proportional to $fracBXCX$? (even though they do not share those sides!)
geometry proof-verification triangles
geometry proof-verification triangles
edited 2 hours ago
YuiTo Cheng
2,48341037
asked 2 hours ago
dragonkingdragonking
384
edited 2 hours ago
YuiTo Cheng
2,48341037
asked 2 hours ago
dragonkingdragonking
384
edited 2 hours ago
YuiTo Cheng
2,48341037
edited 2 hours ago
YuiTo Cheng
2,48341037
edited 2 hours ago
YuiTo Cheng
2,48341037
2,48341037
asked 2 hours ago
dragonkingdragonking
384
asked 2 hours ago
dragonkingdragonking
384
asked 2 hours ago
dragonkingdragonking
384
384
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$A_triangle AXB: A_triangle AXC=BX:CXRightarrow A_triangle AXB=fracBXCXA_triangle AXC$
$A_triangle PXB: A_triangle PXC=BX:CXRightarrow A_triangle PXB=fracBXCXA_triangle PXC$
Hence $$fracA_triangle A X B -A _triangle P X BA _triangle A X C-A_ triangle P X C=fracfracBXCXA_triangle AXC-fracBXCXA_triangle PXCA _triangle A X C-A_ triangle P X C=fracBXCX$$
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3190589%2funderstanding-cevas-theorem%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$A_triangle AXB: A_triangle AXC=BX:CXRightarrow A_triangle AXB=fracBXCXA_triangle AXC$
$A_triangle PXB: A_triangle PXC=BX:CXRightarrow A_triangle PXB=fracBXCXA_triangle PXC$
Hence $$fracA_triangle A X B -A _triangle P X BA _triangle A X C-A_ triangle P X C=fracfracBXCXA_triangle AXC-fracBXCXA_triangle PXCA _triangle A X C-A_ triangle P X C=fracBXCX$$
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
$endgroup$
add a comment |
$begingroup$
$A_triangle AXB: A_triangle AXC=BX:CXRightarrow A_triangle AXB=fracBXCXA_triangle AXC$
$A_triangle PXB: A_triangle PXC=BX:CXRightarrow A_triangle PXB=fracBXCXA_triangle PXC$
Hence $$fracA_triangle A X B -A _triangle P X BA _triangle A X C-A_ triangle P X C=fracfracBXCXA_triangle AXC-fracBXCXA_triangle PXCA _triangle A X C-A_ triangle P X C=fracBXCX$$
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
$endgroup$
add a comment |
$begingroup$
$A_triangle AXB: A_triangle AXC=BX:CXRightarrow A_triangle AXB=fracBXCXA_triangle AXC$
$A_triangle PXB: A_triangle PXC=BX:CXRightarrow A_triangle PXB=fracBXCXA_triangle PXC$
Hence $$fracA_triangle A X B -A _triangle P X BA _triangle A X C-A_ triangle P X C=fracfracBXCXA_triangle AXC-fracBXCXA_triangle PXCA _triangle A X C-A_ triangle P X C=fracBXCX$$
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
$endgroup$
$A_triangle AXB: A_triangle AXC=BX:CXRightarrow A_triangle AXB=fracBXCXA_triangle AXC$
$A_triangle PXB: A_triangle PXC=BX:CXRightarrow A_triangle PXB=fracBXCXA_triangle PXC$
Hence $$fracA_triangle A X B -A _triangle P X BA _triangle A X C-A_ triangle P X C=fracfracBXCXA_triangle AXC-fracBXCXA_triangle PXCA _triangle A X C-A_ triangle P X C=fracBXCX$$
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
answered 2 hours ago
YuiTo ChengYuiTo Cheng
2,48341037
2,48341037
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3190589%2funderstanding-cevas-theorem%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
