The length of AB = b - a , MN = 3a - b/2 and MP = b/2 + (k + 1)( b - a)
It is given that OB = b and OA = a
From ΔAOB we have
OB + BA + AO = 0
b + (- AB ) -a = 0
AB = b - a
Now from ΔMNO we get
MN + NO + OM = 0
MN + ( -ON) + OB/ 2 = 0
MN - (OA + AN ) + b/2 = 0
MN - ( a + 2a) + b/2 = 0
MN = 3a - b/2
Now from ΔMBP , we have
MB + BP + PM = 0
OB/2 + (BA - PA) + PM = 0
b/2 + ( - AP/k + AP) + PM = 0
b/2 + ( -kAB /k + kAB) + PM = 0
b/2 + ( k AB + AB ) + PM ) = 0
PM = -b/2 - (k + 1) (b - a)
MP = b/2 + ( k+1) (b - a)
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