Section 9-2 Tangents

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. radius tangent Right angle

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. This is the converse of theorem 9-1. Point of tangency

. Example 1 Use R with tangent OT to complete: 1.) If OR = 6 and OT = 8, then RT = _____. 2.) If m<OTR = 45, and OT = 4, then RT = _____. 3.) If RO = 5, and OT = 12 then ET = _____. R E O T

Corollary Tangents to a circle from a point are congruent C Segment AC is congruent to Segment AB B

Inscribed and Circumscribed Circumscribed about the circle When a polygon has all sides being a tangent of a circle

Inscribed and Circumscribed Inscribed in the polygon The same situation as before, the polygon has a circle inside that meets each side at a point of tangency

Common tangents With two circles we draw an invisible line connecting the centers A common tangent that crosses this line is an internal tangent A common tangent that does not cross this line is an external tangent external internal

Example 2…think about it… What do you think is true about common internal tangents RS and TU? R U G RG = TG S + GS = GU T RG + GS = TG + GU RS = TU

Tangent Circles Two circles can be tangent to each other if they share exactly one point Internally tangent Externally tangent

. . Example 3 Name a line that satisfies the given description 1.) tangent to P but not to Q. 2.) Common external tangent to both circles 3.) Common internal tangent A B Q P W E C D

Example 4 . . In the diagram, M and N are tangent at P. PR and SR are tangents to N. N has diameter 16, PQ = 3, and RQ = 12 1.) PM = ____ 2.) MQ = ____ 3.) PR = ____ 4.) SR = ____ 5.) NS = ____ 6.) NR = ____ . . R P Q M N S

HW: pg 335-336 (1-11) The End