Circle

Answer

Infinite number of circles can pass through one point. Any point on a plane can be the circumference of countless circles with different radii and centers.

Answer

Infinite number of circles can pass through two distinct points. All these circles will have their centers lying on the perpendicular bisector of the line segment joining the two points.

Answer

There is exactly one unique circle that passes through three non-collinear points. This circle is called the circumcircle of the triangle formed by the three points.

Answer

A tangent to a circle is a line that touches the circle at exactly one point. This point is called the point of contact or point of tangency.

Answer

A secant to a circle is a line that intersects the circle at exactly two points. The two points of intersection are called the endpoints of the secant.

Answer

Tangent Theorem: A tangent to a circle is perpendicular to the radius at the point of contact. If line l is tangent to circle with center O at point P, then l ⊥ OP.

Answer

Converse of Tangent Theorem: A line perpendicular to a radius at its point on the circle is a tangent to the circle. If line l ⊥ radius OP at point P on the circle, then l is tangent to the circle.

Answer

Exactly two tangents can be drawn to a circle from any external point. These two tangent segments from the external point to the points of contact are equal in length.