Chitra657 wrote:
Bunuel wrote:
In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above
I'm totally not able to visualize how making a circle bigger and bigger would still ensure that the circle will keep passing through the two points given. Could you please explain that and also why the centre of the circle will always be on y axis in a bit more detail, im very confused.
Additionally, is there any circle simulations available where I could just punch in numbers to see how the radius of circle differs but it keeps passing through the same points (like the slope simulation that is available on google)
VeritasKarishma Bunuel ScottTargetTestPrep BrentGMATPrepNowmikemcgarryConsider the line joining (4, 0) and (-4, 0). Since both its end points lie on the circle, the line is a chord.
Now consider the case when this chord is the diameter of the circle. Then radius of the circle is 4.
But what if the chord is not the diameter but a small chord in the circle? Then its radius will be much greater.
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Consider that A is (-4, 0) and B is (4, 0).
The black circle will have a radius of 4. The red circle will have greater radius. The green circle will have even greater radius.
and so on... The chord can be infinitesimally small compared with the circle and hence the radius can be as large as we wish.