COMMENT ⊗   VALID 00005 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	{≤GP93W0,750,100,1900λ25JUFA}
C00004 00003	L560,700C5I∂10,∂20}L{I∂0,∂-120}≤a≥{L560-320,690}a{
C00006 00004	L400,-300C160C5
C00007 00005	L400,-700C160,-150*π/180,300*π/180C5
C00008 ENDMK
C⊗;
{≤G;P93;W0,750,100,1900;λ25;JUFA}
\In order to put the iron triangle
into the tripod, the  edge BC is first placed
between the tripod legs of angle ≤a≥.  Let
a  be the length of BC, likewise b and c
are the lengths of AC and AB.


\Restricting attention to the plane LBC,
consider the locus of points L' arrived at
by sliding the  tripod  and  maintaining
contacts at B and C.


\Remembering that in a circle,  a chord
subtends equal angles at all points of each
arc on either side of the chord; it can be  seen
that the  set of possible L' points lie
on a  circular  arc.  Let  this  arc be called  L's  arc,  which  is part of L's
circle.



\Also in a circle the angle at the center
is   double    the    angle    at    the
circumference, when the rays forming the
angles meet  the  circumference  in  the
same two points.





\And  the  perpendicular  bisector  of  a
chord passes  thru  the  center  of  the
chord's  circle  bisecting  the  central
angle. Let S be the distance between the
center of the circle and the chord BC.
So by trigonometric definitions:
{JC} R  =  a / 2sin(≤a≥)
{JC} S  =  R cos(≤a≥)
{H3;
L560,700;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-320,690;}a{
L560,700,560-350,700+94;
L560,700,560-350,700-94;
L560,700;C50,165*π/180,30*π/180;
L400-138,700+80;C5;I∂-10,∂-5;}B{
L400-138,700-80;C5;I∂30,∂-5;}C{
L400-138,700+80,400-138,700-80;

L560,400;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-320,390;}a{
L560,400,560-350,400+94;
L560,400,560-350,400-94;
L560,400;C50,165*π/180,30*π/180;
L400-138,400+80;C5;I∂-10,∂-5;}B{
L400-138,400-80;C5;I∂30,∂-5;}C{
L400-138,400+80,400-138,400-80;
L502,522;C5;I∂0,∂10;}L'{
L502-70,522-35;}≤a≥{
L502,522;C50,190*π/180,30*π/180;
L502,522,502-345,522-60;
L502,522,502-268,522-225;

L560,100;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-315,90;}a{
L560,100,560-350,100+94;
L560,100,560-350,100-94;
L560,100;C50,165*π/180,30*π/180;
L400-138,100+80;C5;I∂-10,∂-10;}B{
L400-138,100-80;C5;I∂30,∂-10;}C{
L400-138,100+80,400-138,100-80;
L502,222;C5;I∂0,∂10;}L'{
L502-70,222-35;}≤a≥{
L502,222;C50,190*π/180,30*π/180;
L502,222,502-345,222-60;
L502,222,502-268,222-225;
L400,100;C160;
L400,-300;C160;C5;
C50,150*π/180,60*π/180;I∂10,∂-90;}2≤a≥{
L400,-300,400-138,-300+80;
L400,-300,400-138,-300-80;
L560,-300;C5;I∂10,∂20;}L{I∂0,∂-120;}≤a≥{L560-315,-310;}a{
L560,-300,560-350,-300+94;
L560,-300,560-350,-300-94;
L560,-300;C50,165*π/180,30*π/180;
L400-138,-300+80;C5;I∂-10,∂-10;}B{
L400-138,-300-80;C5;I∂30,∂-10;}C{
L400-138,-300+80,400-138,-300-80;

L400,-700;C160,-150*π/180,300*π/180;C5;
L400-80,-700-30;}S{
L400-80,-700+50;}R{
L400-190,-700+25;}a/2{
L400,-700;
C50,150*π/180,30*π/180;I∂-10,∂-75;}≤a≥{

L400-138,-700+80;C5;I∂-10,∂-10;}B{
L400-138,-700-80;C5;I∂30,∂-10;}C{
L400-138,-700-80,400-138,-700+80,400,-700;
L400-138,-700,400+160,-700;

W0,1260,100,1800;λ30}