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Find the center of the sphere inscribed in the tetrahedron x=0,y=0,z=0,x+2y+2z=1

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Find the center of the sphere inscribed in the tetrahedron x=0,y=0,z=0,x+2y+2z=1

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Let (a,b,c) be the Centre and r, the radius of the sphere.
The sphere is inscribed in the tetrahedron, hence the length of the perpendicular from the centre (a,b,c) upon each of the faces = radius of the sphere

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