Practice 8A 1. What is the value of x? 2. What is m(arc DE)? 5. If central angle is 65°, what is the measure of the major arc whose end points are at the intersection of the central angle and the circle. 8. What is m∠ABC? 4. What is m∠SRQ? 6. In the given figure, O is the center of 7. In the circle with center O, what is the circle. What is m∠QPR, if m∠
m∠ABD? OQR = 47°? Practice 8B 1. Which of the following is true about a diameter that bisects a chord? A. It is congruent to the chord. B. It is parallel to the chord. C. It is perpendicular to the chord. D. The diameter and chord intersect on the circle. 3. In circle with center O, which arc is intercepted by ∠ABC? 9. What is (x+y)? 10. What is the value of a? 2. Segment PT is tangent to circle O at T. What is the value of r? 3. Point O is the center of the circle. Assume the lines that appear to be tangent are tangent. What is the value of x? 4. Point O is the center of the circle. Assume the lines that appear to be tangent are tangent. What is the value of x? 5. Point O is the center of the circle. 6. In the figure, what is the value of x Assume the lines that appear to be to the nearest tenth? tangent are tangent. What is the value of x? 7. A 9-­‐cm chord is 11 cm from the center of a circle. What is the radius of the circle? 10. What is the value of x? 8. The radius of a circle is 10.8 ft. The length of a chord is 12 ft. What is the approximate distance of the chord from the center of the circle? 9. The diameter of a circle is 25 cm and a chord of the same circle is 16 cm. To the nearest tenth, what is the distance of the chord from the center of the circle? Practice 8C 1. What is the value of x? 2. Identify the appropriate relationship among x, y, and z in the figure. A. x+y+z=90° B. x+y+z=180° x+z
C. y =
2
!
y+z
D. x =
2
!
3. Given a circle with two secants as shown at the right. What is the value of the arc designated by x? 4. Rob wants to take a picture of a fountain. His camera is at the vertex of the angle formed by the tangents to the fountain. If Rob estimates that this angle is 30°, what is x, the measure of the arc of the fountain that will be in the photograph? 5. Two chords intersect within a circle to form an angle whose measure is 53°. If the intercepted arcs are represented by 3x+3 and 10x–14, find the measure of larger of these two arcs. Practice 8D 1. What is the value of x in the diagram? 2. What is the value of d in the diagram? 4. What is the value of x to the nearest tenth? Practice 8E 1. What is the approximate area of a circle with radius 6 cm? 3. A museum window is formed by adding a semicircle to the top of a rectangle. The base of the rectangle is 2 ft. What is the area of the semicircular part of the window? Round your answer to the nearest tenth. 3. In the figure, two secants have a common endpoint outside the circle. What is the approximate value of z? 5. Given the circle with two intersecting chords. What is the length represented as x? 2. What are the circumference and area of a circle with radius 11 m? Round your answers to the nearest tenth. 4. What is the area of the quarter circle if the radius is 5 m? 5. The circle at the center of a basketball court has an area of 113 square ft. Which is the best estimate of the radius of the circle? 6. A circle with radius 12 and a rectangle with width 16 have equal areas. Which of the following must be true? I. The perimeter of the rectangle is 56. II. The area of the circle and rectangle is 56. III. The length of the rectangle is 9π. A. I only B. II only C. III only D. II and III E. I, II, and III 7. What is the approximate area of a circle with a 9. A dart hits the dartboard shown. circumference of 15 in.? What is the probability that it lands in the shaded region? 8. If the area of a square inscribed in a circle is 16 10. A dart hits the dartboard square cm, what is the area of the circle in square shown. What is the probability that cm? it lands in a circle? Practice 8F 1. The shaded region of circle P represents one-­‐eighth of the area of the circle. What is the measure of the central angle of the region? 2. What is the length of an arc whose measure is 60° if the radius of the circle is 12 cm? Leave your answer in terms of π. 3. The radius of a circle is 12 cm. What is the length of a 60° arc? 4. A circle has area 72π square yards. What is the area of a 10° sector of the circle? 5. A sector of 90° has area π square mm. What is the area of the circle? Practice 8G 1. In the circle with center O, line DK is 2. What is m∠ACB? 3. Which expression the tangent at C. What is m∠BCK? represents m(arc BE)? A. 360-­‐a-­‐2b-­‐2c B. 360-­‐a-­‐b-­‐c C. 360-­‐2a-­‐2b-­‐c D. 360+2a+2b+c E. None of these 4. What is m∠ACB? 8. Point O is the center of the circle. Assume the lines that appear to be tangent are tangent. What is the value of x? 5. What is the value of x in the diagram? 6. What is the approximate area of a circle with diameter 8 cm? 7. What is the circumference of a circle with radius 9? 9. Given the circle below with two tangents to the circle from a common external point. What is the measure of the angle designated by x? 10. In the diagram at the right, secant segment AB intersects circle O at D, secant segment AC intersects circle O at E, AE=4, AC=24, and AB=16. What is AD? Practice 8H 1. 2. 3. 4. 6. 5. Practice 8I 1. In the circle with center O, line DP is the tangent at C. What is m∠ACD? 2. What is the value of x? 3. What is the approximate circumference of a circle with diameter 9 in.? 4. To the nearest tenth, what is the value of x? 5. A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section? Express answer to the nearest square foot. 6. If rays QP and QR are tangent to circle O at P and R, and m∠OQR=32°, what is m∠POQ? 7. In the diagram, the segments shown are tangent to the circle. What is the value of x? 8. A 240° arc has length 16π ft. What is 9. In the diagram of circle O, chord AB the radius of the circle? intersects chord CD at E, DE=2x+8, EC=3, AE=4x−3, and EB=4. What is the value of x? 10. In the diagram below of circle O, secant segment AB intersects circle O at D, secant segment AC intersects circle O at E, AE=4, AB=12, and DB=6. What is the length of segment OC?