Question

In Fig. 6, AD $\perp$ BC and BD = $\frac{1}{3}$ CD. Prove that 2CA² = 2AB² + BC²

Answer 1

In the given figure, we have

and, then we have to prove

The following given diagram is

Now, suppose the value of BD is x, then

In triangle ADC, we have

…… (1)

And in triangle ADB, we have

…… (2)

Now add the equation (1) and equation (2), we get

…… (3)

Now we are putting the values of BD and CD, we get

Hence proved.