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The incenter of a triangle is the point of intersection of all the perpendicular bisectors of the sides of a triangle. 

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Important Questions on Altitudes and Medians of a triangle

HARD
If G is the centroid of a ABC and P is any other point in the plane, then PA2+PB2+PC2 is equal to
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Point G is the centroid of  ABC.

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If l(RG) = 2.5, then l(GC) = _____

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The medians of a triangle cross each other at _____.
MEDIUM
If the centroid of the triangle formed by the points (3,-5), (-7,4), (10,-k) is at the point (k,-1), then k=
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Medians of a triangle meet at a point. The point is called _____.

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The median of a triangle is the line segment joining any of its vertices to the _____ of the opposite side.

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The vertices of a triangle are (0, 0), (3, 0) and (0, 4). The centroid of the triangle is
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(Perimeter of a triangle) _____ (Sum of its three medians).  <,>,=

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Point G is the centroid of  ABC. If l(BG)=6 units then l(BQ) = _____ units.

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In the triangle ABC,

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The median is _____(CF, BE, AD) .

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 The centroid is the point of concurrency of the _____of a triangle.
MEDIUM
If (-2,1) is the centroid of the triangle having its vertices at (x,2), (10,-2), (-8,y), then x, y satisfy the relation
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The centroid of a triangle divides each medians in the ratio _____.
MEDIUM
In ABC, D is the midpoint of BC.
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AD is the _____.
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Sum of any two sides of a triangle _____ twice the median to the 3rd side. <,>,=

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Intersection point of the medians of triangles is called _____.

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Median of a triangle is the segment that joins the vertex to the _____ of the opposite side.