Presentation on theme: "9 – 2 Tangent. Tangents and Circles Theorem 9 – 1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of."— Presentation transcript:
Tangents and Circles Theorem 9 – 1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. ZT O m Given m is tangent to O at T then OT m
Tangents and circles Corollary Tangents to a circle from a point are congruent. A B P In the figure PA and PB are tangent to the circle at A and B. By the corollary, PA = PB
Tangents and Circles Theorem 9 – 2 If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle R Q l Given: Line l is in the plane of Q l radius QR at R. Then l is tangent to Q
Tangents and Circles When each side of a polygon is tangent to a circle, the polygon is said to be circumscribed about the circle and the circle is inscribed in the polygon.
Tangents and Circles A line that is tangent to each of two coplaner circles is called a common tangent. A common internal tangent intersects the segments joining the centers. A B AB is a common internal tangent
Tangents and Circles A common external tangent does not intersect the segment the segment joining the centers R S RS is a common external tangent
Tangents and Circles A circle can be tangent to a line but it can also be tangent to another circle. Tangent circles are coplaner circles that are tangent to the same circle. Externally tangent circles Internally tangent circles