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sorry for the bad drawing credit to @dan815
are you sure its true, its seems hard to believe
Yes it is true, verified with geogebra
\(a\) and \(b\) need to be on the same side of the line
oh here is something
we are dealing with 2 sets of parallel slopes here
Well, c = y sinw , a = y sin ( w - 60) , b = y sin(w +60 ) we have to prove that a + b = c left: a + b = ysin(w-60) + ysin(w+60) = y( sin(w-60)+ sin(w+60)) = y[ sinwcos60 - coswsin60 + sinwcos60 + coswsin60] = y* 2sinwcos60 = ysinw = c
@ganeshie8 , here is the proof. Get the other part from the last question
that works @TrojanPoem !
trying to not jump into algebra, wanna see if theres a more pure geometry proof
exactly ^ there is a really short proof w/o using trig, and looks you had a good start dan
@ganeshie8 , Like++. Nice animation.
3 sets of similar triangles
with sides a b a+b
hey is the motion like a pendulum?
is that a perfect arc
is think this is a parallelogram with a triangle inscribed
AC // BD. CD//AB
wow looks like it, nice imagination dan
kind of neat haha, if this relationship defined a pedulum motion in a roundabout way
but it cannot be a circle because the length of that top red segment is changing continuously right
ya thats true, a calculus solution to this might look interesting too, something to look for later
let me know if you want me to share my solution because i see now it wont spoil anything as there can be multiple solutions
You gave up guys ?
nope, we have ur solution so including mine, technically i have 2 solutions... that is far from giving up :D
Come check the new problem, I am stuck with it.
have you posted it already
you're right @dan815 the points do trace circles http://gyazo.com/603ef78cc5a38da14adf431b35db870f
I did. But i think it's invisible