Math, asked by Sabbir22711, 1 year ago

In an acute angled triangle abc ad is the median on the side bc .Prove that 4ad²=2ab²+2ac²-bc²

Answers

Answered by apsnaruka1267
2

Answer:


Step-by-step explanation:Draw AE perpendicular to BC.


Since angle AED = 900,


Therefore, in triangle ADE


angle ADE 900


Thus, triangle ABD is obtuse angled triangle and triangle ADC is acute angled triangle.


Triangle ABD is obtuse angled at D and AE is perpendicular to BD produced,


Therefore,


AB2 = AD2 + BD2 + 2 BD x DE ?????(i)


Triangle ACD is acute angled at D and AE is perpendicular to BD produced,


Therefore,


AC2 = AD2 + DC2 - 2 DC x DE


AC2 = AD2 + BD2 - 2 BD x DE ???(ii) (since CD = BD)


Adding (i) and (ii)


AB2 + AC2 = 2(AD2 + 2BD2)


AB2 +AC2 = 2(AD2 + BD2)


Answered by goraigopal385
1

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