- #1
sachin patil
- 1
- 0
I want to find out the co-ordinate of point of contact of tangent to a circle from external point when its center and radius are known. Please Help me . . .
Thank you in advance . . .
Thank you in advance . . .
Point of contact of circle an tangent
In summary, the conversation discusses finding the coordinates of the point of contact of a tangent to a circle from an external point, given the center and radius of the circle. It is suggested to draw a line from the given point to the center of the circle, find the midpoint, and draw a circle with the line as diameter. The point where this circle intersects the given circle is the tangent point. The conversation also mentions solving for x and y simultaneously in the equations y=mx+k and (x-a)^2+(y-b)^2=r^2, which can be done in terms of the constants m, k, a, b, and r.
- #2
Svein
Science Advisor
- 2,298
- 796
- #3
Mentallic
Homework Helper
- 3,802
- 95
What happens when you simultaneously solve
[tex]y=mx+k[/tex]
[tex](x-a)^2+(y-b)^2=r^2[/tex]
For x and y? They'll be in terms of the m,k,a,b,r constants, but it can be done.
[tex]y=mx+k[/tex]
[tex](x-a)^2+(y-b)^2=r^2[/tex]
For x and y? They'll be in terms of the m,k,a,b,r constants, but it can be done.
1. What is the definition of a point of contact of a circle and a tangent?
A point of contact is the point at which a tangent line touches a circle. It is the only point where the two objects intersect.
2. How is the point of contact of a circle and a tangent calculated?
The point of contact can be calculated using the formula x = x1 + r cosθ and y = y1 + r sinθ, where (x1, y1) is the center of the circle, r is the radius, and θ is the angle between the tangent and the horizontal axis.
3. What is the significance of the point of contact in geometry?
The point of contact is important in determining the slope of the tangent line, which is perpendicular to the radius of the circle at that point. It is also used in various geometric proofs and constructions involving circles and tangents.
4. Can a circle have more than one point of contact with a tangent?
No, a tangent line can only intersect a circle at one point, making it the point of contact. However, a circle can have multiple tangents, each with its own point of contact.
5. How is the point of contact related to the radius of the circle?
The point of contact lies on the circle's circumference and is always perpendicular to the radius at that point. This means that the radius and the tangent line share the same point of contact, forming a right angle.
Similar threads
-
General Math
-
General Math
-
General Math
-
General Math
-
General Math
-
General Math
-
General Math
-
General Math
-
General Math
-
General Math