Question

Let O be the centre of the circle x² + y² = r², where r > √5/2. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle OPQ lies on the line x + 2y = 4, then the value of r is _____ 

Answer 1

Method - II

r² = 4

r = 2

Answer 2

Finding the value of ‘r’:

Given Equation of Circle is,

\(x^ 2+y^2=r^2.r> \frac{\sqrt{5}}{2}\)

‘O’ is the Centre of a circle.

PQ is the chord of this circle and the Equation of

PQ is 

PQ = 2x + 4y = 5

C is the Centre of a Circumcircle of triangle OPQ 

which lies on a line x + 2y = 4

Now,

Therefore,

This C lies on the line x + 2y = 4,

Therefore,

Therefore the radius of a Circle x² + y² = r² is equal to 2.