The shortest distance of a point is always the perpendicular distance. The projection of the point (a,b,c) on the x-axis is (a,0,0). This distance is given by √b2+c2.
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If a + b + c = 2s, then prove the following identities
(a) s2 + (s β a)2 + (s β b)2 + (s β c)2 = a2 + b2 + c2
(b) a2 + b2 β c2 + 2ab = 4s (s β c)
(c) c2 + a2 β b2 + 2ca = 4s (s β b)
(d) a2 β b2 β c2 + 2ab = 4(s β b) (s β c)
(e) (2bc + a2 β b2 β c2) (2bc β a2 + b2 + c2) = 16s (s β a) (s β b) (s β c)