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ICSE Class 9 Answered

In an equilateral triangle, ABC, D is a point  on the side BC such that BD:DC is = 1:3 . Prove that 16 AD^2 = 13 AB^2.
Asked by bsap6777 | 28 Aug, 2018, 09:41: PM
answered-by-expert Expert Answer
Drop AE perpendicular to BC
begin mathsize 18px style AB space equals space BC space equals space AC space equals straight a in space increment space AED AD squared equals DE squared plus AE squared.......... straight A now space height space in space equilateral space increment space equals space fraction numerator square root of 3 over denominator 2 end fraction straight a..... side space opp space to space 60 degree DE space equals space BE space minus space BD equals straight a over 2 minus straight a over 4........ straight D space divides space BC space in space 1 colon 3 equals straight a over 4 so space sub space in space straight A AD squared space equals 13 over 16 straight a squared 16 AD squared space equals 13 straight a squared 16 AD squared space equals 13 AB squared end style
Answered by Arun | 29 Aug, 2018, 11:02: AM

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