Q8 of 13 Page 96

AB is the hypotenuse of the isosceles right triangle AB. AD is the bisector of ∠BAC and AD intersects BC at D. Let’s prove AC + CD = AB.



Let BC = AC = a and CD = b
In a right-angled triangle BCA,


By Pythagoras theorem,


AB2 = BC2 + AC2


AB2 = a2 + a2
AB = a√2
Given AD = b, we get
DB = BC – CD or DB = a – b
We have to prove that AC + CD = AB


or (a + b) = a√2.
By the angle bisector theorem, we get














C + CD = AB [we know that AC = a, CD = b and AB = a√2]
Hence proved.


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