in triangle abc D is the midpoint of side bc ab=7 ac=5 and ad=5 then bc=
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The question is incomplete. The generic solution is given below.
Consider the triangle ABC with A as origin and AB along X-axis.
Since AB =7, Coordinates of B = (7,0)
C could be any point on the circle of radius 5 with center as A. Let the coordinates of C = (x,y) such that x2+y2=52=25
D is the midpoint of BC. Therefore the coordinates of D = (x+72,y2)
AD=(7+x2)2+(y2)2−−−−−−−−−−−−−−−√=49+x2+14x+y24−−−−−−−−−−−−−−−−√
⟹AD=49+14x+254−−−−−−−−−−−−√=14x+74−−−−−−−√2
A special case would be if ABC were right triangle at A:
⟹x=0⟹AD=74−−√2
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