Circles. 1. In the accompanying figure, the measure of angle AOB is 50. Find the measure of inscribed angle ACB.


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1 ircles Name: Date: 1. In the accompanying figure, the measure of angle AOB is 50. Find the measure of inscribed angle AB. 4. In the accompanying diagram, P is tangent to circle at and PAB is a secant. If P = 8 and PA = 4, find AB. 2. Two tangents to a circle from an external point intercept a major arc of 300. Find the number of degrees in the angle formed by the two tangents. 5. In the accompanying diagram, BD is tangent to circle O at B, B is a chord, and BOA is a diameter. If ma : mb = 1 : 4, find m DB. 3. In the accompanying diagram, AB is a diameter of circle O and chord D intersects diameter AB at E. If mad = 100 and ma = 40, find m DEB. page 1
2 6. In the diagram below, chords AB and D intersect at E. If m AE = 4x, ma = 120, and mdb = 2x, what is the value of x? 8. ircle O with AO and AB is shown in the diagram below. A. 12 B D. 60 What is the ratio of m AO to m AB? A. 1 : 1 B. 2 : 1. 3 : 1 D. 1 : 2 7. In the accompanying diagram, tangent PA and secant PB are drawn to circle O from point P. If ma = 80 and mab = 60, what is the measure of P? A. 10 B D In the accompanying diagram, PA is tangent to circle O at A. If B = 12 and PB = 4, what is the length of PA? A. 4 3 B D. 8 page 2 ircles
3 10. In the accompanying diagram of circle O, chords AB and D intersect at point E. If AE = 2, D = 9, and E = 4, find BE. 12. In the accompanying diagram of circle O, diameter AB is perpendicular to chord D and intersects D at E, AE = 9, and EB = 4. What is ED? A. 8 B D In the accompanying diagram, circle O is inscribed in AB so that the circle is tangent to AB at F, to B at E, and to A at D. If AF = FB = 5 and D = 7, find the perimeter of AB. 13. In the diagram below, two parallel lines intersect circle O at points A, B,, and D, with mab = x + 20 and md = 2x 20. Find mab. page 3 ircles
4 14. In the diagram of circle O, diameter AB is parallel to chord D. 16. A circle is drawn to represent a pizza with a 12 inch diameter. The circle is cut into eight congruent pieces. What is the length of the outer edge of any one piece of this circle? A. 3π 4 B. π. 3π 2 D. 3π If md = 70, what is m A? A. 110 B D In the diagram of circle A shown below, chords D and EF intersect at G, and chords E and FD are drawn. 15. In circle R shown below, diameter DE is perpendicular to chord ST at point L. Which statement is not always true? Which statement is not always true? A. SL = TL B. RS = DR. RL = LE D. DL)LE) = SL)LT) A.. G = FG B. EG = FDG E EG = FD DG D. EG FDG page 4 ircles
5 18. In the diagram below, quadrilateral ABD is inscribed in circle P. 20. In the diagram below, D, A, DOB, B, and AB are chords of circle O, FDE is tangent at point D, and radius AO is drawn. Sam decides to apply this theorem to the diagram: An angle inscribed in a semicircle is a right angle. What is m AD? Which angle is Sam referring to? A. 70 B D. 110 A. AOB B. BA. DB D. FDB 19. In circle O shown below, diameter A is perpendicular to D at point, and chords AB, B, AE, and E are drawn. 21. In the diagram below of circle O with diameter B and radius OA, chord D is parallel to chord BA. Which statement is not always true? A. AB = BD B. AB = AD. BA = DB D. BA = AE If m BD = 30, determine and state m AOB. page 5 ircles
6 22. In the diagram below of circle O, OB and O are radii, and chords AB, B, and A are drawn. 24. In the diagram below, DA tangent and secant DB are drawn to circle O from external point D, such that A = B. Which statement must always be true? A. BA = BO B. m BA = 1 2 m BO. BA and BO are isosceles. If mb = 152, determine and state m D. D. The area of BA is twice the area of BO. 25. In the diagram below, mab = A circle whose center is the origin passes through the point 5, 12). Which point also lies on this circle? A. 10, 3) B. 12, 13). 11, 2 12) D. 8, 5 21) What is the number of degrees in the measure of AB? A. 134 B D. 46 page 6 ircles
7 26. In the diagram below of circle O, chord DF bisects chord B at E. If B = 12 and FE is 5 more than DE, then FE is A. 13 B D. 4 page 7 ircles
8 ProblemAttic format version c EducAide Software Licensed for use by Terms of Use at ircles 5/1/ B A B D A A or an equivalent radian measure is found, and appropriate work is shown, such as a labeled diagram. B D B
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