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Find DE^2 (Important For RMO)

Sujoy Das
06/02/2018 0 0

Question:

 

Solution:

AD + AE = 25
AD = x
AE = 25-x

1/2(Area of triangle ABC) = Area of triangle ADE

1/2 ( 1/2× 16×18×SinA) = 1/2 *(25-x)x * SinA

=> x = 9 = AD

25-x = 16 = AE

9²+16²-DE²/(2×9×16) = 16²+18²-20²/(2× 16× 18)

337-DE² = 90

DE² = 247

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