Exploring Circle Tangents: Solving Geometry Problems

1. Ch 11 mini Unit

2. LearningTarget 11-1 Tangents • I can use tangents to a circle to find missing values in figures.

3. A Tangent to a Circle is a line in the plane of a circle that intersects the circle in exactly one point. This point is called the point of tangency.

4. If a line is tangent to a circle, then the line is perpendicular to the radius drawn at the point of tangency • This gives us a Right triangle, so We need to recall Right triangle properties

5. Find x

6. Find x

7. Find x

8. Find x

9. Find x

10. Inscribed or Circumscribed • Do you remember the difference?

11. Two points tangent to a circle from a point outside the circle are congruent

12. Find the perimeter of the triangle

13. Find the perimeter

14. Homework p.586 #1-19 odd skip 5

15. Warmup p.589

16. Learning Target 11-2/11-3 • You will be able to use properties of chords to find missing values • You will be able to use the Inscribed Angle Theorem to find missing angles and arcs

17. Chord – a segment whose endpoints are on a circle • Within a circle or in congruent circles • Congruent central angles have congruent chords • Congruent Chords have congruent arcs • Congruent arcs have congruent central angles

18. Within a circle, • Chords equidistant from the center are congruent • Congruent chords are equidistant from the center

19. Find x

21. More properties of chords • In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs • The reverse (converse) of this is true also

26. The measure of an inscribed angle is half the measure of its intercepted arc. • Pic/example

27. Properties of Inscribed Angles • Two inscribed angles that intercept the same arc are congruent • An angle inscribed in a semicircle is a right angle • The opposite angles of a quadrilateral inscribed in a circle are supplementary. • Examples p. 600

28. The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. • Pic/example

33. Homework • P.593-594 #3-19 odd skip 9 • P. 601 1-19 odd

34. WARMUPp. 605 Checkpoint QUIZ

35. Learning Target 11-4 • I can find measures of angles formed by chords, secants, and tangents.

36. A secant is a line that intersects a circle at two points. • We are going to use secants, tangents, and chords to solve problems See p.607

40. Rules on page 609

41. Learning target 11-5 • I can write the equation of a circle

42. An equation of a circle in a coordinate plane • + • (h,k) is the center, and r is the radius

43. Identify the center and the radius

46. Graph

47. Review • P.700 1-19, 21-23 • P.627 6,7,89-12, 13-15, 16-21