Question #06bcd

1 Answer
Sep 13, 2015

its simple

Explanation:

Draw AE perpendicular to BC.

Since angle AED = 900,

Therefore, in triangle ADE

angle ADE < 900 and angle ADB > 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,

#AB^2 = AD^2 + BD^2 + 2 BD * DE # ...... #(i)#

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

Therefore,

#AC^2 = A^D2 + DC^2 - 2 DC * DE#

#AC^2 = AD^2 + BD^2 - 2 BD * DE # ........#(ii) #

(since, CD = BD)

Adding (i) and (ii)

#AB^2 + AC^2 = 2AD^2 + 2BD^2#

#AB^2 +AC^2 = 2(AD^2 + BD^2)#