Question

Prove that in a triangle, other than equilateral traingle, angle opposite to longest side is greater than 2/3 the third side

Answer 1

LET AB = AD = DB

●ABD is a equilateral triangle..

SINCE

=> AB = AD = BD
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=> angle(ABD) = angle(ADB) = angle(BAD) = 60

Longest side = BC

●Angle opposite to longest side = angle(BAC)

HERE,

●It is clear that :-

angle(BAC) = angle(BAD) = angle(CAD)

SO,

=> angle(BAC) > angle(BAD)

=> angle(BAC) > 60

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=> 2/3 of right angle = 2/3 × 90 = 60

SO,

●angle(BAC) > 2/3 of right angle
____________________[◢PROVED]

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