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# Geometry

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Intern
Joined: 13 Feb 2009
Posts: 21

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27 Feb 2009, 04:32
What is the value ON/AN in the triangle ABC?
1. AM=MB
2. CN=NB

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Intern
Joined: 23 Feb 2009
Posts: 6

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27 Feb 2009, 08:45
IMO C
if AM=MB and BN=NC then CM and AN both are medians
there is a rule.. when medians in triangle crosses in one point, they divided in ratio 2:1 from the apex
so ON/AN = 1/3

am i right?? this rule not only for quilateral triangle?
VP
Joined: 05 Jul 2008
Posts: 1333

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27 Feb 2009, 19:00
I could not solve it But I can say that this is an equilateral triangle. I chose C because it seemed that there is a property by means of which there is a relation between ON and AN

AM=MB means the the line/altitude of the corresponding base is bisecting the base. So the other two sides are equal. AC=BC

From 2 AB=AC

Put together we have AB=AC=BC.

Now the point where all the medians intersect is called centroid. So N is clearly the centroid.

Thats where I could not move further but chose C as there seems to be a relationship between the lengths between the vertex and centroid and centroid and mid point of the side.
SVP
Joined: 07 Nov 2007
Posts: 1733
Location: New York

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27 Feb 2009, 22:00
A segment that joins a vertex of a triangle and the midpoint of the side opposite that vertex is called a median. The three medians are concurrent at the centroid (the point of their intersection, and it is two-thirds of the way down each median. For example, if the three medians AA', BB', and CC' of the triangle ABC, intersect at G, then AG = 2GA', BG = 2BG', and CG = 2CG')

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Manager
Joined: 17 Dec 2008
Posts: 162

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28 Feb 2009, 10:56
Centroid properties
===============
Centroids splits the medians in the ratio 1:2
Centroids splits triangle into 6 triangles with equal area.
VP
Joined: 17 Jun 2008
Posts: 1477

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28 Feb 2009, 17:12
x2suresh wrote:
A segment that joins a vertex of a triangle and the midpoint of the side opposite that vertex is called a median. The three medians are concurrent at the centroid (the point of their intersection, and it is two-thirds of the way down each median. For example, if the three medians AA', BB', and CC' of the triangle ABC, intersect at G, then AG = 2GA', BG = 2BG', and CG = 2CG')

Is this the property of an equilateral triangle or any type of triangle? I could not comprehend how this could be true for a triangle that has three unequal sides.
Intern
Joined: 01 Mar 2009
Posts: 40

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03 Mar 2009, 00:23
is there a "quality" book that contains advanced geometry properties? (and maybe algebra?)

thanks!

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Re: Geometry   [#permalink] 03 Mar 2009, 00:23
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# Geometry

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