The diameter of the larger circle must be equal to the distance between the centers of the two circles plus twice the radius of the smaller circle.
Let A be the center of the smaller circle.
Using the Pythagorean theorem, we can find the distance between the centers of the two circles.
Let's call the distance between the centers of the two circles as d.
In right triangle CTA, where C and A are the centers of the big and small circles respectively, and T is the point of intersection, we have:
(d/2)^2 + 4^2 = d^2
(d^2)/4 + 16 = d^2
(d^2)/4 - d^2 = -16
-d^2/4 = -16
d^2/4 = 16
d^2 = 64
d = 8
Therefore, the distance between the centers of the two circles is 8.
The diameter of the larger circle is equal to 8 + 2 * 4, which is 16.
Therefore, the diameter of the larger circle must be 16.
Two circle intersect at point T, if the small circle radius is 4 and C is the center of the big circle, then the biameter of the larger circle must be
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