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anonymous
 one year ago
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anonymous
 one year ago
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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439559062484:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not all of them will pass through the center though...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Notice that the center of circle is the "circumcenter" of the triangle we're working on

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1so basically the problem is equivalent to finding the triangles such that the circumcenter lies interior to the triangle

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1for what triangles do we have circumcenter interior to the triangle ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yes, they would be all "acute" triangles so our job is to find the number of acute triangles and divide them by 84

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1we may use the relation between inscribed angle and central angle : \(\theta = \dfrac{\alpha}{2}\) dw:1439560115696:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1not really sure how to approach this, im still thinking..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks so much for helping me, sir. But I must go to sleep now, its getting late for me. I will think about this tomorrow.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Okay, have good sleep :) I'll try to post the solution over the night, pretty sure this is not that hard...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks so much! i really appreciate it!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Consider vertex A. From AB, we have 7 triangles, and among them just ABF has center inside of it. That is the probability to get the center inside of the triangle is 1/7 for vertex A Same for others Hence the total is 1/7^9 but we have to subtract the overlap parts. I meant \(\triangle ABC\) when consider node A will be overlap with \(\triangle BCA\) for node B.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Hence for node B, we have 1 triangle overlaps with node A for node C, we have 1triangles overlaps with node A \(\triangle ACD\), and 1 triangle overlaps with nod B \(\triangle CBA\) Same for other nodes and same argument, we have the logic 1st node 0 overlap 2nd node1 overlap 3rd node2 overlap ::::::::::::::::::::::::::::::: 9th node8 overlap  total 36 cases.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Ok, part 1) is done, now just calculate the possibility of it.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1for part a, im getting \(\dfrac{30}{84}\) for partb, the general formula for probability is \(\dfrac{n+1}{2(2n1)}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you tell me how, i need to write an explanation with my answer...
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