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How can you prove that the line between to points is a tangent of the smaller circle?
Step I: Show that both points are outside the smaller circles. Possibly by showing that distance from each point to the centre of the circle is greater than its radius.
Step 2: Show that the line between the two points touches the circle at exactly one point. This would be by simultaneous solution of the equations of the line and the circle.
What else can I help you with?
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
What is a line in the plane of a circle that intersects the circle at two points?
tangent
A secant tangent passes through the center of a circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Line intersecting a circle in two points?
A line can be tangent to a circle in which case it intersects it in one point, it can intersect it in two points, or no points at all. So the choices are 0,1 or 2.
How many points does a tangent line have in common with its circle?
one and only one point no matter how far produced.
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
What is a line in the plane of a circle that intersects the circle at two points?
tangent
A tangent line is a line that intersects a circle at exactly two points?
No. A tangent touches the circle at exactly one point. A line that intersects a circle at exactly two points is a secant.
How many points does a tangent line touch a circle?
1
A secant tangent passes through the center of a circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Does a secant tangent angle pass through the center of the circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
Does a tangent to a circle intersect the circle in 2 points?
No, only at one point, perpendicular to the radius
Shortest distance between two points on the earth?
The two points and the centre of the earth define a plane, and the intersection of this plane with the surface of the earth is a circle - the "Great Circle". The shortest distance between the two points is the smaller of the two arcs on this circle.
What is the name of a straight line joining any two points on the circumference of a circle?
Tangent
Can a line be tangent to one circle and a secant to the other in concentric circles?
Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.
What is a line called that intersects a circle at one point?
A tangent line. A line that intersects a circle at two points is a secant.
Line intersecting a circle in two points?
A line can be tangent to a circle in which case it intersects it in one point, it can intersect it in two points, or no points at all. So the choices are 0,1 or 2.
