anik89 wrote:
The center of a circle is (5, -2). (5, 7) is outside the circle, and (1, -2) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
The center of a circle is (5, -2)As we can see from the image below, there are infinitely many circles that have their center at (5, -2)
(1, -2) is INSIDE the circleWe can quickly determine that the distance from (1, -2) to the circle's center (5, -2) is 4 units...
So a circle with a radius of 4 would PASS THROUGH the point (1, -2).
Since (1, -2) is INSIDE the circle, we know that
the radius of the circle must be GREATER THAN 4(5, 7) is OUTSIDE the circleThe distance from (5, 7) to the circle's center (5, -2) is 9 units...
So a circle with a radius of 9 would PASS THROUGH the point (5, 7).
Since (5, 7) is OUTSIDE the circle, we know that
the radius of the circle must be LESS THAN 9So, we now have lower and upper limits of the radius.
The radius of the circle is GREATER THAN 4 and LESS THAN 9In other words,
4 < r < 9Since the radius, r, is an INTEGER, there are only four possible values of r.
r can equal 5, 6, 7, or 8
Answer:
Cheers,
Brent
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