Point of Contact Between Arc and Circle

In summary, the point of contact between an arc and a circle is where they intersect, and it can be calculated using the intersection point formula. This point is significant in geometry and can help solve problems related to tangents, secants, and chords. There can be more than one point of contact between an arc and a circle, and the radius of the circle does not affect the point of contact as long as the centers are the same. If the centers are different, the radius of the circle will determine the location of the point of contact.
  • #1
mjgarrin
9
0
Hello,
I have an arc with an arc length = 46.88 mm and radius = 44 mm.
I have an intersecting arc with an arc length = 26.69 mm and radius = 43.4 mm.

A circle with radius = 24 mm fits between the two arcs.

How can I determine the contact points of the circle and the two arc lines?
 
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  • #2
Do you know the position and orientation of those arcs? Do you know (or can you calculate) where their corresponding circle centers are?

You can determine the central point of the 24mm-circle as a function of the contact points, and see if you can set both points equal.
 

1. What is the point of contact between an arc and a circle?

The point of contact between an arc and a circle is the single point where the arc and the circle intersect.

2. How is the point of contact between an arc and a circle calculated?

The point of contact between an arc and a circle can be calculated using the intersection point formula, which involves finding the equations of the arc and the circle and then solving for the coordinates of the intersection point.

3. What is the significance of the point of contact between an arc and a circle in geometry?

The point of contact between an arc and a circle is significant in geometry because it helps to establish the relationship between the two shapes and can aid in solving problems related to tangents, secants, and chords.

4. Can there be more than one point of contact between an arc and a circle?

Yes, there can be more than one point of contact between an arc and a circle. This occurs when the arc and the circle intersect at multiple points.

5. How does the radius of the circle affect the point of contact with an arc?

The radius of the circle does not affect the point of contact with an arc, as long as the circle and the arc have the same center. However, if the circle and the arc have different centers, the radius of the circle will determine where the point of contact is located.

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