If G is the centroid and I the in-centre of the triangle, with vertices A(-36,7), B(20,7) and C(0,-8), then, find the value of GI.

I am afraid you are looking for a trick to solve this problem but there is no one

go by the longer route

first calculate the centroid

dropping a line from (-36,7) to the mid point of BC and using the property of 2:3 of centroid.

now calculate the incentre

find a perpendicular to AB with an asrbitrary constant k1(I think you can calculate that much)

find another perpendicular to BC with an arbitrary constant k2

and so for the case of AC

find their intersection point of AB and BC such that the distance between the point of intersection and the lines is same.

repaet

now find the distance betwen the incentre and centroid

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