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DaalChawal
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Help in circle touching internally all these three circles.
What is the internal tangent circle problem for three given circles?
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In summary, "circle touching internally" refers to the position of two circles where one circle is completely inside the other circle, and they are touching at one point. Two circles can touch internally when the radius of the smaller circle is equal to the distance between the center of the larger circle and the point of contact. This is different from "circle intersecting," which means that the circles have at least two points in common. Two circles of different sizes can touch internally as long as the radius of the smaller circle is equal to the distance between the center of the larger circle and the point of contact. The mathematical equation for determining if two circles are touching internally is if the distance between the centers of the two circles is equal to the sum of their
Help in circle touching internally all these three circles.
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Opalg
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In the diagram, the three given circles are the red one with centre $(6,8)$ and radius $5$, the blue one with centre $(-12,9)$ and radius $10$, and the green one with centre $(0,-8)$ and radius $3$. It should be easy to see that the circle which touches all three of them externally is the purple one with centre at the origin and radius $5$. But it is altogether harder to locate the black circle which touches all three of them internally. In fact, I doubt whether it is possible to find an exact solution. The best I can do is a numerical approximation that gives its centre as $(-5.912,5.002)$ and its radius as $17.283$.
In the diagram, the three given circles are the red one with centre $(6,8)$ and radius $5$, the blue one with centre $(-12,9)$ and radius $10$, and the green one with centre $(0,-8)$ and radius $3$. It should be easy to see that the circle which touches all three of them externally is the purple one with centre at the origin and radius $5$. But it is altogether harder to locate the black circle which touches all three of them internally. In fact, I doubt whether it is possible to find an exact solution. The best I can do is a numerical approximation that gives its centre as $(-5.912,5.002)$ and its radius as $17.283$.
FAQ: What is the internal tangent circle problem for three given circles?
What is meant by "circle touching internally"?
"Circle touching internally" refers to a scenario where two circles intersect in such a way that one circle is completely contained within the other, without any part of the circles overlapping or intersecting on the outside.
How can you determine if two circles are touching internally?
To determine if two circles are touching internally, you can use the distance formula to find the distance between the centers of the circles. If the distance between the centers is equal to the difference between the radii of the circles, then they are touching internally.
What is the formula for finding the distance between the centers of two circles?
The formula for finding the distance between the centers of two circles is d = √((x2-x1)^2 + (y2-y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the centers of the circles.
Can two circles touch internally at more than one point?
No, two circles can only touch internally at one point. If they touch at more than one point, then they are overlapping or intersecting on the outside, which is not considered as "touching internally".
What are some real-life examples of circles touching internally?
Some real-life examples of circles touching internally include concentric circles on a dartboard, the rings of a target in archery, and the layers of an onion. In each of these examples, one circle is completely contained within the other without any overlap or intersection on the outside.