Prove that $AD cdot AD' = AE cdot AE'$. Announcing the arrival of Valued Associate #679: Cesar...
String `!23` is replaced with `docker` in command line
Using audio cues to encourage good posture
How widely used is the term Treppenwitz? Is it something that most Germans know?
Why did the Falcon Heavy center core fall off the ASDS OCISLY barge?
Echoing a tail command produces unexpected output?
How does debian/ubuntu knows a package has a updated version
How to react to hostile behavior from a senior developer?
What is Arya's weapon design?
Output the ŋarâþ crîþ alphabet song without using (m)any letters
Using et al. for a last / senior author rather than for a first author
How to find all the available tools in mac terminal?
Book where humans were engineered with genes from animal species to survive hostile planets
Why is "Consequences inflicted." not a sentence?
Can a non-EU citizen traveling with me come with me through the EU passport line?
How to align text above triangle figure
Identifying polygons that intersect with another layer using QGIS?
Identify plant with long narrow paired leaves and reddish stems
Why is my conclusion inconsistent with the van't Hoff equation?
What does the "x" in "x86" represent?
How do pianists reach extremely loud dynamics?
3 doors, three guards, one stone
English words in a non-english sci-fi novel
Check which numbers satisfy the condition [A*B*C = A! + B! + C!]
List *all* the tuples!
Prove that $AD cdot AD' = AE cdot AE'$.
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How I can show that the point P (Miquel point) is in the circle formed by the centers of the other 4 circles?Prove that $SC=SP$ if and only if $MK=ML.$Prove concurrency in a triangleGeometry. How to solve this problem?Prove that line $EB$ is tangent to the circumcircle of triangle $ADF$ at point $B$.Heights and circumcircleFour circles tangent to each other and an equilateral triangleTangency in the Mixtilinear Incircle ConfigurationProve: the ratio between the areas of $ABC$ and $AB'C'$ is $AB'cdotfrac{AC'}{(AC cdot AB)}$Circum-centre of triangle formed by external bisectors of base angles of a given triangle is collinear with the other vertices of the two triangles.
$begingroup$
Circle diameter $BC$ cuts side $AB$ and $AC$ of $triangle ABC$ respectively $C'$ and $B'$. $E$ and $E'$ are points respectively on $BC$ and the circumcircle of $AB'C'$ such that $EE'$ passes through $A$ and $EE'$ cuts the circle diameter $BC$ at $D$ and $D'$. Prove that $AD cdot AD' = AE cdot AE'$.
I tried proving that $AE cdot AE' = AM^2$ with $AM$ is a tangent of the circle diameter $BC$.
geometry euclidean-geometry circles
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
$endgroup$
add a comment |
$begingroup$
Circle diameter $BC$ cuts side $AB$ and $AC$ of $triangle ABC$ respectively $C'$ and $B'$. $E$ and $E'$ are points respectively on $BC$ and the circumcircle of $AB'C'$ such that $EE'$ passes through $A$ and $EE'$ cuts the circle diameter $BC$ at $D$ and $D'$. Prove that $AD cdot AD' = AE cdot AE'$.
I tried proving that $AE cdot AE' = AM^2$ with $AM$ is a tangent of the circle diameter $BC$.
geometry euclidean-geometry circles
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
$endgroup$
add a comment |
$begingroup$
Circle diameter $BC$ cuts side $AB$ and $AC$ of $triangle ABC$ respectively $C'$ and $B'$. $E$ and $E'$ are points respectively on $BC$ and the circumcircle of $AB'C'$ such that $EE'$ passes through $A$ and $EE'$ cuts the circle diameter $BC$ at $D$ and $D'$. Prove that $AD cdot AD' = AE cdot AE'$.
I tried proving that $AE cdot AE' = AM^2$ with $AM$ is a tangent of the circle diameter $BC$.
geometry euclidean-geometry circles
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
$endgroup$
Circle diameter $BC$ cuts side $AB$ and $AC$ of $triangle ABC$ respectively $C'$ and $B'$. $E$ and $E'$ are points respectively on $BC$ and the circumcircle of $AB'C'$ such that $EE'$ passes through $A$ and $EE'$ cuts the circle diameter $BC$ at $D$ and $D'$. Prove that $AD cdot AD' = AE cdot AE'$.
I tried proving that $AE cdot AE' = AM^2$ with $AM$ is a tangent of the circle diameter $BC$.
geometry euclidean-geometry circles
geometry euclidean-geometry circles
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
edited Mar 24 at 12:01
Michael Rozenberg
111k1897201
111k1897201
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
asked Mar 24 at 11:38
Lê Thành ĐạtLê Thành Đạt
47313
47313
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$measuredangle ECB'=measuredangle AC'B'=measuredangle AE'B',$$ which says that $EE'B'C$ is cyclic.
Id est, $$AD'cdot AD=AB'cdot AC=AE'cdot AE$$ and we are done!
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
$endgroup$
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%2f3160436%2fprove-that-ad-cdot-ad-ae-cdot-ae%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
$begingroup$
$$measuredangle ECB'=measuredangle AC'B'=measuredangle AE'B',$$ which says that $EE'B'C$ is cyclic.
Id est, $$AD'cdot AD=AB'cdot AC=AE'cdot AE$$ and we are done!
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
$endgroup$
add a comment |
$begingroup$
$$measuredangle ECB'=measuredangle AC'B'=measuredangle AE'B',$$ which says that $EE'B'C$ is cyclic.
Id est, $$AD'cdot AD=AB'cdot AC=AE'cdot AE$$ and we are done!
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
$endgroup$
add a comment |
$begingroup$
$$measuredangle ECB'=measuredangle AC'B'=measuredangle AE'B',$$ which says that $EE'B'C$ is cyclic.
Id est, $$AD'cdot AD=AB'cdot AC=AE'cdot AE$$ and we are done!
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
$endgroup$
$$measuredangle ECB'=measuredangle AC'B'=measuredangle AE'B',$$ which says that $EE'B'C$ is cyclic.
Id est, $$AD'cdot AD=AB'cdot AC=AE'cdot AE$$ and we are done!
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
answered Mar 24 at 12:00
Michael RozenbergMichael Rozenberg
111k1897201
111k1897201
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%2f3160436%2fprove-that-ad-cdot-ad-ae-cdot-ae%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
