A) (3.5, 9.5)
B) \[(-7,7)\]
C) (-10,1)
D) \[(-10,1)\]
Correct Answer: B
Solution :
Here, as shown in the figure, point (6, 8) is on the circumference of the circle. Distance of \[(6,8)\] from the origin \[(0,0)\] will be the radius of the circle. Radius of circle \[O=\sqrt{{{(8-0)}^{2}}+{{(6-0)}^{2}}}\] \[=\sqrt{{{8}^{2}}+{{6}^{2}}}\] \[=\sqrt{100}\] \[=10\] Now, points with the distance of 10 from the origin or center of circle lies on the circumference of the circle and points with distance of less than 10 from origin or center of the circle lies within the circle. So, we have to find a point whose distance from origin is less than 10. By checking all the options we can see that, distance between \[(-7,7)\] and \[(0,0)\] \[D=\sqrt{{{(7-0)}^{2}}+{{(-7-0)}^{2}}}\] \[=\sqrt{49+49}\] \[=\sqrt{98}<0\] So, the point \[(-7,7)\] lies within the circle.
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