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9 – 2 Tangent

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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

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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

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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

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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.

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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

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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

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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

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