Question

if triangle ABC,right angle B which is 90 degree,AB=BC, BC is produced to a point D . Prove that AD2= 2BC.BD+CD2 ......Pls help me friends​

Answer 1

Step-by-step explanation:

bthe midpoint of BC= AD = CD.

Angle B is a right angled triangle.

Consider ΔABC

AC^2 = AB^2 + BC^2 [Pythagoras theorem]

⇒ AC2 = AB^2 + (2BD)^2  (BC=BD+DC,BD=DC,So we can replace BC by 2BD.

⇒ AC^2 = AB^2 + 4BD^2 ----------- (1)

Consider ΔABC

AD^2 = AB^2 + BD^2 [Pythagoras theorem] ----------- (2)

Subtracting equation (2) from (1), we get

⇒ AC^2 - AD^2 = 3BD^2

⇒ AC^2 - AD^2 = 3CD^2 [  BD = CD,So we can replace BD by CD]

⇒ AC^2 = AD^2 + 3CD^2

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