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Question

Let O be the centre of the circle x2+y2=r2where r>52.


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Solution

Finding the value of ‘r’:

Given Equation of Circle is,

x2+y2=r2,r>52

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,

PQ:hx+ky=x2

2x+4y=5h=2,k=4,r2=5.

h2=k4=r25h=2r25,k=4r25

Therefore,

Cr25,2r25

This C lies on the line x+2y=4, therefore,

r25+22r25=4

r215+45=4

r255=4

r2=4r=2

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


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