Name: _________________________________________________________ 14-11 Circles Review Geometry Pd. ______ Date: __________

14-11: Circles Review

Station 1: Circle Equations

1. Write the equation of a circle with a radius of √5 units and a center (3,-2). 2. Identify the center and radius of the following circle. Leave answers in simplest radical form.

𝑥2 + (𝑦 + 5)2 = 50 3. Use the following equation for parts a-c a) Write the equation in center-radius form b) Identify the center and radius of the circle

center: __________ radius: ___________ c) Graph the circle → 4. Write the equation of the circle graphed below:

5. Write the equation of a circle whose center is (2,1) and passes through the point (2,-3) 6. Graph the following circle: 7𝑥2 + 7𝑦2 = 448

Station 2: Systems 7. Solve the following System of equations graphically:

16 = (x-2)2 +(y+3)2 y + x = -5 State the number of solutions.

Station 3: Area of a Sector/Arc Length

8. a. Segment NM is 3.5 in. Find the area of the shaded region to the nearest whole number

b. Find the length of minor arc MO to the nearest inch. 9. The area of sector FHE is 156.38 𝑦𝑑2. Find the area of Circle H to the nearest 10th. 10. a) The length of minor arc SQ is 3.82 in. Find the circumference of circle R to the nearest inch.

b) What is the radius of circle R to the nearest tenth?(use your final answer from part A)

11. In a circle whose radius is 10 ft., what is the length of the arc intercepted by a central angle of 4 radians?

Station 4: Circle Theorems

12. In the accompanying diagram of circle O, and . What is the measure of ?

1) 1040

2) 800

3) 520

4) 400

13. In the accompanying diagram of circle O, chord is parallel to diameter , is drawn, and m𝐴�̂� = 80. What is ?

14. In the accompanying diagram of circle O, chords and intersect at E and

. What is ?

15. In the diagram below, is tangent to circle O, and is a chord. If , find the measure of .

1) 90

2) 40

3) 130

4) 100

16. Tangents and are drawn from point to the same circle. The major arc intercepted by the tangents is three

times the minor arc. Find .

17. In the accompanying diagram, is tangent to circle O at Q and is a secant. If and ,

find .

18. In the accompanying diagram of circle O, , is a diameter, and radius is drawn. If ,

find .

19.

20. In the accompanying diagram of circle O, secant and intersect at C. If , , and

, find EC.

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

. Find x

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

23. In the accompanying diagram, , , and are tangent to circle

O at F, E, and G, respectively. If , , and , find BC.

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

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

26. In the accompanying diagram of circle O, PBA and PCD are secants, chords AC and BD intersect at E,

𝐵𝐴̅̅ ̅̅ ≅ 𝐶𝐷̅̅ ̅̅ , chord BC is drawn, m∠𝐴𝐵𝐷 = 65 𝑑𝑒𝑔𝑟𝑒𝑒𝑠, 𝑎𝑛𝑑 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑎𝑟𝑐 𝐵𝐶 𝑖𝑠 60 𝑑𝑒𝑔𝑟𝑒𝑒𝑠.

Find:

a) m<ACD

b) m<P

c) m<DBC

d) m<ACP

Station 5: Circle Proofs

27. in circle O at the right. Prove that

28. In the accompanying diagram of circle O, AD is a diameter with AD parallel to chord BC, chords AB and

CD are drawn, and chords BD and AC intersect at E.

Prove: BE ̅̅ ̅̅ ≅ CE ̅̅ ̅̅

29. In the accompanying diagram of circle O, diameter EOD is drawn, tangent AF is drawn to the circle at C,

B is a point on the circle, and ∠𝑂𝐴𝐶 ≅ ∠𝐸𝐷𝐵.

Prove: ∆𝑂𝐴𝐶 ~∆𝐸𝐷𝐵.