1. Geometry Chapter 9 Review

2. Secant A line that contains a chord of a circle. SECANT.P.P

3. Tangent A line in the plane of a circle that intersects the circle in exactly one point..P.P. Point of tangency

4. Theorem If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. ●

5. Corollary Tangents to a circle from a point are congruent. ● ●

6. Theorem In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent. If m 1 = m 2, then JK = LM. M J 2 1 K 77 ~ If JK = LM, then m 1 = m 2. 77 ~ k m 1 2

7. Theorem Theorem In the same circle or in congruent circles: congruent arcs have congruent chords congruent chords have congruent arcs ● O

8. Theorem Theorem A diameter that is perpendicular to a chord bisects the chord and its arc. ● O

9. Theorem Theorem In the same circle or in congruent circles: chords equally distant from the center (or centers) are congruent congruent chords are equally distant from the center (or centers) ● O

10. Inscribed Angle Theorem The measure of the inscribed angle is half the measure of its central angle (and therefore half the intercepted arc). 30 o 60 o

11. A Very Similar Theorem The measure of the angle created by a chord and a tangent equals half the intercepted arc. 70 o t a n g e n t c h o r d 35 o

12. Corollary If two inscribed angles intercept the same arc, then the angles are congruent. xy x = y ~ sf giants sf = giants ~

13. Corollary If an inscribed angle intercepts a semicircle, then it is a right angle. diameter Why? diameter 180 o 90 o

14. Corollary If a quadrilateral is inscribed in a circle, then opposite angles are supplementary. 70 o 110 o 95 o 85 o supplementary

15. If mAD = 50 and mBC = 60 Interior Angle Theorem Interior Angle Theorem The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs. A B C D 1 m<1 = ½( mAD + mBC ) 50˚ 60˚ m<1 = ½(50 + 60) = _____ 55

16. Exterior Angle Theorem Exterior Angle Theorem The measure of the angles formed by intersecting secants and tangents outside a circle is equal to half the difference of the measures of the intercepted arcs. 1 y˚ x˚ m<1 = ½(x – y) 2 y˚ x˚ m<2 = ½(x – y) 3 y˚ x˚ m<3 = ½(x – y)

17. Theorem When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord. X P S Q R 8 34 6 x 8 x 3 = 6 x 4

18. Theorem When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment. G H F D E FD x FE = FH x FG External x Whole Thing = External x Whole Thing

19. Theorem When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment. When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment. B P C A PB x PC = (PA) 2 External x Whole Thing = (Tangent) 2

20. HW: Start After You Finish the Ch.8 Quiz Chapter 9 W.S. Chapter 9 W.S.