File:Schiffler theorem.svg

Original file(SVG file, nominally 454 × 404 pixels, file size: 40 KB)

Summary

Description
English: Schiffler theorem: then the Euler lines of triangles BIC, CIA and AIB have a common point S
Date
Source Own work
Author Rocchini

Source Code

Made with Carmetal, source code is:

<?xml version="1.0" encoding="utf-8"?>
<CaR>
<Construction>
<Window x="4.666517379490333" y="2.2903089505656187" w="15.999999999999998"/>
<Windowdim w="1112" h="944"/>
<Preferences minfontsize="30" minpointsize="4" minlinesize="2" arrowsize="10" selectionsize="8" monkeyspeed="20" gridopacity="20" digits.lengths="2" digits.edit="4" digits.angles="2" colorbackground="255,255,255" colorbackgroundx="4" colorbackgroundy="3" colorbackgroundPal="4" fig3D="false" figDP="false"/>
<Objects>
<Point name="A" n="0" color="2" type="thick" showname="true" bold="true" large="true" x="-1.5331516802906453" y="3.2552225249772926" shape="circle">Punto</Point>
<Point name="C" n="1" color="2" type="thick" showname="true" x="-7.532076759076176" y="-7.491199089905666" shape="circle">Punto</Point>
<Point name="B" n="2" color="2" type="thick" showname="true" x="12.372119551853402" y="-6.285151254260299" shape="circle">Punto</Point>
<Point name="P2" n="1305" color="2" hidden="true" x="-2.303360581289737" y="3.7347865576748402" shape="circle">Punto</Point>
<Segment name="s1" n="5" color="4" type="thick" from="A" to="C">Segmento da A a C</Segment>
<Segment name="s2" n="8" color="4" type="thick" from="C" to="B">Segmento da C a B</Segment>
<Segment name="s3" n="11" color="4" type="thick" from="B" to="A">Segmento da B a A</Segment>
<Angle name="a1" n="397" color="1" hidden="super" showvalue="true" unit="°" first="B" root="A" filled="true" fixed="angle180(a(B,A,C))/2">Angolo B - A di musura angle180(a(B,A,C))/2</Angle>
<Circle name="c1" n="398" color="4" hidden="super" through="B" midpoint="A" acute="true">Circonferenza di centro A per B</Circle>
<Angle name="a2" n="876" color="1" hidden="super" showvalue="true" unit="°" first="A" root="C" filled="true" fixed="angle180(a(A,C,B))/2">Angolo A - C di musura angle180(a(A,C,B))/2</Angle>
<Circle name="c2" n="877" color="4" hidden="super" through="A" midpoint="C" acute="true">Circonferenza di centro C per A</Circle>
<Angle name="a3" n="1253" color="1" hidden="super" showvalue="true" unit="°" first="A" root="B" filled="true" fixed="angle180(a(A,B,C))/2">Angolo A - B di musura angle180(a(A,B,C))/2</Angle>
<Circle name="c4" n="1254" color="4" hidden="super" through="A" midpoint="B" acute="true">Circonferenza di centro B per A</Circle>
<Midpoint name="P9" n="1275" color="2" type="thin" first="C" second="B" shape="circle">Punto medio tra C e B</Midpoint>
<Midpoint name="P10" n="1278" color="2" type="thin" first="B" second="A" shape="circle">Punto medio tra B e A</Midpoint>
<Midpoint name="P11" n="1281" color="2" type="thin" first="A" second="C" shape="circle">Punto medio tra A e C</Midpoint>
<Intersection name="P4" n="399" hidden="super" showname="true" first="a1" second="c1" shape="circle" which="first">Intersezione tra a1 e c1</Intersection>
<Intersection name="P5" n="878" hidden="super" showname="true" first="a2" second="c2" shape="circle" which="first">Intersezione tra a2 e c2</Intersection>
<Intersection name="P1" n="1255" hidden="super" showname="true" first="a3" second="c4" shape="circle" which="first">Intersezione tra a3 e c4</Intersection>
<Plumb name="p4" n="1306" color="3" hidden="true" point="P2" line="s1" valid="true">Retta perpendicolare per P2 a s1</Plumb>
<Ray name="r1" n="400" color="3" type="thin" from="A" to="P4">Semiretta da A puntando a P4</Ray>
<Ray name="r2" n="879" color="3" type="thin" from="C" to="P5">Semiretta da C puntando a P5</Ray>
<Ray name="r3" n="1256" color="3" type="thin" from="B" to="P1">Semiretta da B puntando a P1</Ray>
<Intersection name="I" n="880" color="3" type="thick" showname="true" first="r1" second="r2" shape="circle">Intersezione tra r1 e r2</Intersection>
<Plumb name="p3" n="1262" color="5" type="thin" point="B" line="r1" valid="true">Retta perpendicolare per B a r1</Plumb>
<Plumb name="p6" n="1312" color="5" type="thin" point="C" line="r3" valid="true">Retta perpendicolare per C a r3</Plumb>
<Plumb name="p7" n="1316" color="5" type="thin" point="A" line="r2" valid="true">Retta perpendicolare per A a r2</Plumb>
<Plumb name="p1" n="883" color="5" type="thin" point="I" line="s1" valid="true">Retta perpendicolare per I a s1</Plumb>
<Plumb name="p2" n="1259" color="5" type="thin" point="I" line="s3" valid="true">Retta perpendicolare per I a s3</Plumb>
<Midpoint name="P3" n="1266" color="2" type="thin" first="I" second="B" shape="circle">Punto medio tra I e B</Midpoint>
<Midpoint name="P6" n="1269" color="2" type="thin" first="A" second="I" shape="circle">Punto medio tra A e I</Midpoint>
<Midpoint name="P8" n="1272" color="2" type="thin" first="I" second="C" shape="circle">Punto medio tra I e C</Midpoint>
<Segment name="s4" n="1284" color="1" type="thin" from="I" to="P10">Segmento da I a P10</Segment>
<Segment name="s6" n="1291" color="4" type="thin" from="I" to="P9">Segmento da I a P9</Segment>
<Segment name="s8" n="1298" color="1" type="thin" from="I" to="P11">Segmento da I a P11</Segment>
<Plumb name="p5" n="1309" color="5" type="thin" point="I" line="s2" valid="true">Retta perpendicolare per I a s2</Plumb>
<Segment name="s10" n="1332" color="1" type="thick" from="A" to="I">Segmento da A a I</Segment>
<Segment name="s11" n="1335" color="1" type="thick" from="I" to="B">Segmento da I a B</Segment>
<Segment name="s12" n="1338" color="1" type="thick" from="I" to="C">Segmento da I a C</Segment>
<Angle name="a4" n="1341" color="1" xcoffset="0.6096743844436752" ycoffset="0.7045841128553265" unit="°" first="A" root="C" second="I" display="normalsize" filled="true" acute="true">Angolo A - C - I</Angle>
<Angle name="a5" n="1346" color="1" xcoffset="0.9054251147737814" ycoffset="0.2198794867007534" unit="°" first="I" root="C" second="B" display="normalsize" filled="true" acute="true">Angolo I - C - B</Angle>
<Angle name="a6" n="1349" color="1" xcoffset="-0.9296774541666047" ycoffset="0.06197949942684754" unit="°" first="C" root="B" second="I" display="normalsize" filled="true" acute="true">Angolo C - B - I</Angle>
<Angle name="a7" n="1352" color="1" xcoffset="-0.8043935832686243" ycoffset="0.4702048386939088" unit="°" first="I" root="B" second="A" display="normalsize" filled="true" acute="true">Angolo I - B - A</Angle>
<Angle name="a8" n="1355" color="1" xcoffset="-0.2611000364263463" ycoffset="-0.894409524833598" unit="°" first="I" root="A" second="C" display="normalsize" filled="true" acute="true">Angolo I - A - C</Angle>
<Angle name="a9" n="1358" color="1" xcoffset="0.5837747836606149" ycoffset="-0.7261877368125299" unit="°" first="I" root="A" second="B" display="normalsize" filled="true" acute="true">Angolo I - A - B</Angle>
<Intersection name="P7" n="884" color="1" type="thin" first="p1" second="s1" shape="circle">Intersezione tra p1 e s1</Intersection>
<Intersection name="H1" n="1263" color="2" showname="true" first="p2" second="p3" shape="circle">Intersezione tra p2 e p3</Intersection>
<Segment name="s5" n="1287" color="1" type="thin" from="A" to="P3">Segmento da A a P3</Segment>
<Segment name="s7" n="1294" color="1" type="thin" from="B" to="P8">Segmento da B a P8</Segment>
<Segment name="s9" n="1301" color="2" type="thin" from="C" to="P6">Segmento da C a P6</Segment>
<Intersection name="H2" n="1313" color="2" showname="true" first="p5" second="p6" shape="circle">Intersezione tra p5 e p6</Intersection>
<Intersection name="H3" n="1317" color="2" showname="true" first="p1" second="p7" shape="circle">Intersezione tra p1 e p7</Intersection>
<Intersection name="P13" n="1366" color="2" first="p2" second="s3" shape="circle">Intersezione tra p2 e s3</Intersection>
<Circle name="c3" n="887" type="thin" through="P7" midpoint="I" acute="true">Circonferenza di centro I per P7</Circle>
<Intersection name="M1" n="1288" color="2" showname="true" first="s5" second="s4" shape="circle">Intersezione tra s5 e s4</Intersection>
<Intersection name="M2" n="1295" color="2" showname="true" first="s6" second="s7" shape="circle">Intersezione tra s6 e s7</Intersection>
<Intersection name="M3" n="1302" color="2" showname="true" first="s8" second="s9" shape="circle">Intersezione tra s8 e s9</Intersection>
<Angle name="a11" n="1365" color="1" type="thin" xcoffset="0.8721820628531461" ycoffset="0.3277805308009201" unit="°" first="I" root="P7" second="A" display="small" filled="true" acute="true">Angolo I - P7 - A</Angle>
<Angle name="a12" n="1369" color="1" type="thin" xcoffset="0.44285602712023897" ycoffset="-0.8197683614156991" unit="°" first="I" root="P13" second="B" display="small" filled="true" acute="true">Angolo I - P13 - B</Angle>
<Line name="l1" n="1320" color="2" from="M1" to="H1">Retta per M1 e H1</Line>
<Line name="l2" n="1323" color="2" from="H2" to="M2">Retta per H2 e M2</Line>
<Line name="l3" n="1328" color="2" from="M3" to="H3">Retta per M3 e H3</Line>
<Intersection name="P12" n="1359" color="2" first="s2" second="c3" shape="circle" which="second">Intersezione tra s2 e c3</Intersection>
<Intersection name="S" n="1329" type="thick" showname="true" first="l1" second="l2" shape="circle">Intersezione tra l1 e l2</Intersection>
<Angle name="a10" n="1362" color="1" type="thin" xcoffset="-0.8546213517500604" ycoffset="0.37116569381854453" unit="°" first="I" root="P12" second="C" display="small" filled="true" acute="true">Angolo I - P12 - C</Angle>
</Objects>
</Construction>
</CaR>

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

5 May 2012

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current08:23, 5 May 2012Thumbnail for version as of 08:23, 5 May 2012454 × 404 (40 KB)Rocchini
The following pages on the English Wikipedia use this file (pages on other projects are not listed):