Best Answer

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.

Q: How can you prove that the line between to points is a tangent of the smaller circle?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.

tangent

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.

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.

one and only one point no matter how far produced.

Related questions

A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.

tangent

No. A tangent touches the circle at exactly one point. A line that intersects a circle at exactly two points is a secant.

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.

1

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.

No, only at one point, perpendicular to the radius

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.

Tangent

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.

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.

A tangent line. A line that intersects a circle at two points is a secant.