Atul Dixit
Respected Sir,
Let ABC be a triangle with AD,BE and CF as the medians and with
centroid G.Construct semi -circles with diameters BD,DC and BC all
outwardly.(shoemaker's knife).Let T1 be circle touching the three
semi-circles BD,DC and BC and let A' be the centre of this circle .(It is
easy to prove that the radius of T1 is one-sixth of BC).Similarly define B'
and C' .It seems that AA',BB' and CC' are concurrent .
What is the locus of point P such that AA',BB'and CC' are concurrent ,if we
consider AD ,BE ,CF as the cevians concurrent at P?
Let ABC be a triangle with AD,BE and CF as the medians and with
centroid G.Construct semi -circles with diameters BD,DC and BC all
outwardly.(shoemaker's knife).Let T1 be circle touching the three
semi-circles BD,DC and BC and let A' be the centre of this circle .(It is
easy to prove that the radius of T1 is one-sixth of BC).Similarly define B'
and C' .It seems that AA',BB' and CC' are concurrent .
What is the locus of point P such that AA',BB'and CC' are concurrent ,if we
consider AD ,BE ,CF as the cevians concurrent at P?
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