Name: ____________________________ 13-11 Review Part 2

Geometry Pd. __________ Date: _____

13-5 Parallel Chords

The arcs between two parallel chords are congruent

Congruent Chords

The arcs outside (subtended by) congruent chords are congruent

13-6 Segment Length INSIDE Circle (PP)

If a diameter/radius is perpendicular to a chord, then it bisects that chord.

13-7 Segment Length

OUTSIDE Circle

A right angle is formed at the point of tangency between a tangent and diameter/radius

Tangents that meet at one

exterior point are congruent:

13-8 Big Circles (Yesterday’s Review)!13-9 Circle Proofs Tips

Mark up your diagram Come up with a plan Use your proof pieces Look for congruent angles and congruent sides Always look for radii (always congruent) and Inscribed Angles!!!

Part 1: Segment Length1. In the accompanying diagram of circle O, secant and intersect at C. If , , and , find EC.

part x part = part x partor

pp = pp

whole x outer = whole x outeror

wo = wo

3 common tangents

4 common tangents

2. In the diagram below, is a tangent to circle O at point S, is a secant, , , and . Find x

3. In a circle, chords and intersect at E. If , , and , find CE.

4. In the accompanying diagram, , , and are tangent to circle O at F, E, and G, respectively. If , , and , find BC.

5. In the accompanying diagram of circle O, diameter . and . Find CE and m<ACB

6. In the diagram below, circle A and circle B are shown. Draw in all possible common tangents.

7. In the diagram below of , is tangent to circle O at point A, , and . What is the length of ?

8. Given circles O and M sharing tangent lines AC and AE, the ratio of AB:BC = 3:2. If AE = 35, solve for DE:

9. Given circle O with marked chords, solve AB

Part 2: Proof10. Given: AB ≅AC in circle O Prove that

Statements Reasons1. AB ≅AC in circle O 1. Given

11. Given: AD is a diameter, AD|| BC Prove: BE≅CEStatements Reasons1. 1. Given

12. Given: FB ≅ EB, and AD is tangent to circle O at B.Prove: ∆ OBA ∆ OBC.Statements Reasons

1. FB ≅ EB, and AD is tangent to circle O at B.

1. Given

Part 3: Are you ready for anything? Mixed Review!

13) a) Given that <UTV = 30. What is the measure of TS?

b) What is the measure of UT?

14. In circle , chords and intersect at . If , , and , what is the length of ?1)

2)

3)

4)

15. Modeling with Mathematics: The Cassini spacecraft is on a mission in orbit around Saturn until September 2017. Three of Saturn’s moons, Tethys, Calypso, and Telesto, have nearly circular orbits of radius 295,000 km. The diagram shows the position of the moons and the spacecraft on one of Cassini’s missions. Find the distance DB, to the nearest meter, from Cassini to Tethys when AD is tangent to the circular orbit.

16. In the diagram below of circle O, chord is parallel to diameter and arc CD is 134 degrees.

What is ? Show all work!

Hint: Sketch it!

17. Given: chords and intersect at G, and chords and are drawn.Prove:

18) In the diagram shown below, is tangent to circle T at A, and secant is drawn where point B is on circle T.

If and BC = 12, what is the length of in simplest radical form?

19. In the diagram below, is the diameter of circle A. Point D, a different point from B and C, is plotted on circle A.

a) What type of triangle would have to be? (classify by angles)

b) Explain your answer thoroughly referencing theorems, relationships, proof tools etc.

20) Segments shown are tangents to the circles. Find x. 21) Solve for the arc marked x:

22) Solve for x, showing all steps. 23) Given circle O with tangent at B. AB≅ AC, and

AB :CB=3: 4. Find x.

24) Solve for x: Work hard and Study! go slow, show all work, use color

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