PRMO 2012 question 7


7. In △ABC\triangle ABC, we have AC=BC=7AC = BC = 7 and AB=2AB = 2. Suppose that DD is a point on line ABAB such that BB lies between AA and DD and CD=8CD = 8. What is the length of BD?
[PRE-RMO–2012]

Solution:
Since ABC is an isosceles triangle.
Let's say E is the midpoint of AB.
Then CAB will be a right angle.
Let BD = x.
CE = 7^2 - 1^2 = 8^2 - (1+x)^2
=> 48 = 64 - (1+x)^2
=> x + 1 = 4
=> x = 3
Ans. 3




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