Tangents And Circles Worksheets

How Do Tangents Relate to Circles? Mathematically, a tangent is defined as the line that intersects or touches the circle at exactly one point. The point where the tangent touches the circle is known as the point of tangency. At this point, the tangent lies perpendicularly to the radius. Tangent plays a vital role in geometrical constructions and developing proofs. To know whether the line is tangent or not, we consider the following properties: A tangent line never crosses or passes through the circle. The tangent is always perpendicular to the radius. A tangent and chord form an angle that is of the same measurement as the angle inscribed on the opposite side of the chord. Some of the theorems related to tangents are discussed as under: Tangent to a Circle Theorem - The tangent to a circle theorem states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency. Two Tangents Theorem - The two tangent theorem states that if two tangent segments are drawn from the same external point, then the segments are equal. Tangent Secant Theorem - The tangent secant theorem tells us about the relation of segments created by tangent and secant with an associated circle.