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27 Feb 2009, 04:32
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What is the value ON/AN in the triangle ABC?
1. AM=MB
2. CN=NB
1. AM=MB
2. CN=NB
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27 Feb 2009, 08:45
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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?
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?
27 Feb 2009, 19:00
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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.
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.
