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ganeshie8
 one year ago
show that \(a+b=c\)
where \(a,b,c\) are the perpendicular distances from vertices to a line passing through the centroid of an equilateral triangle as shown :
ganeshie8
 one year ago
show that \(a+b=c\) where \(a,b,c\) are the perpendicular distances from vertices to a line passing through the centroid of an equilateral triangle as shown :

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435678656585:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1sorry for the bad drawing credit to @dan815

dan815
 one year ago
Best ResponseYou've already chosen the best response.1are you sure its true, its seems hard to believe

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes it is true, verified with geogebra

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\(a\) and \(b\) need to be on the same side of the line

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435679309628:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we are dealing with 2 sets of parallel slopes here

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0Well, 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(w60) + ysin(w+60) = y( sin(w60)+ sin(w+60)) = y[ sinwcos60  coswsin60 + sinwcos60 + coswsin60] = y* 2sinwcos60 = ysinw = c

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 , here is the proof. Get the other part from the last question

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1that works @TrojanPoem !

dan815
 one year ago
Best ResponseYou've already chosen the best response.1trying to not jump into algebra, wanna see if theres a more pure geometry proof

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1exactly ^ there is a really short proof w/o using trig, and looks you had a good start dan

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 , Like++. Nice animation.

dan815
 one year ago
Best ResponseYou've already chosen the best response.13 sets of similar triangles

dan815
 one year ago
Best ResponseYou've already chosen the best response.1hey is the motion like a pendulum?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0is think this is a parallelogram with a triangle inscribed

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435680716273:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1wow looks like it, nice imagination dan

dan815
 one year ago
Best ResponseYou've already chosen the best response.1kind of neat haha, if this relationship defined a pedulum motion in a roundabout way

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1but it cannot be a circle because the length of that top red segment is changing continuously right

dan815
 one year ago
Best ResponseYou've already chosen the best response.1ya thats true, a calculus solution to this might look interesting too, something to look for later

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1let me know if you want me to share my solution because i see now it wont spoil anything as there can be multiple solutions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1nope, we have ur solution so including mine, technically i have 2 solutions... that is far from giving up :D

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0Come check the new problem, I am stuck with it.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1have you posted it already

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you're right @dan815 the points do trace circles http://gyazo.com/603ef78cc5a38da14adf431b35db870f

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.0I did. But i think it's invisible
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