Question

in ∆ abc ,bd is median to ac,ab =10 ,bc=8 ,bd=8 then find ac

Answer 1

According to appolonius theorem, AB^2+BC^2=2BD^2+2AD^2 10^2+8^2=2(8)^2+2AD^2 100+64=128+2AD^2 DIVIDING BY 2, 82=64+AD^2 82-64=AD^2 18=AD^2 AD=3√2 Now AC=2AD               =2×3√2          AC=6√2