In Δle ABC , AB2 = AC2+BC2 - 2 AC . BC cos θ AC2+BC2 is max → AB2 + 2 AC BC cos θ is max. But for allpositions of C, AB and O are constants. AC.BC maximum or
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AC.BC sin θ is max. ∴ AC2+BC2 max. implies Δ is max or
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h × AB is maximumor h is maximum → height is the diameter. ∴ AC = CB or Δle is isosceles