Question

In the given figure, ∠B < 90° and segment AD ⊥ BC, show that

(i) $b^2=h^2+a^2+x^2-2ax$
(ii) $b^2=a^2+c^2-2ax$

Answer 1

(i) Since AD perpendicular to BC we obtained two right angled triangles, triangle ADB and triangle ADC.

We will use Pythagoras theorem in the right angled triangle ADC

…......(1)

Let us substitute AD = h, AC = b and DC = (a − x) in equation (1) we get,

…......(2)

(ii) Let us use Pythagoras theorem in the right angled triangle ADB as shown below,

…......(3)

Let us substitute AB = c, AD = h and BD = x in equation (3) we get,

Let us rewrite the equation (2) as below,

…......(4)

Now we will substitute in equation (4) we get,

Therefore, .