Chords and tangents: lengths and right angles

Answer Key - Grade 10 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ren cuts a straight chord across a round pizza. Circle O has radius 13 cm. Chord CF is 12 cm from O, measured at a right angle. How long is CF, in cm?

   10
2. 2.

   Zee sews a straight stripe across a round rug. Circle O has radius 17 cm. Chord CF is 8 cm from O, measured at a right angle. How long is CF, in cm?

   30
3. 3.

   Ari lays a straight path across a round lawn. Circle O has radius 25 m. Chord CF is 7 m from O, measured at a right angle. How long is CF, in m?

   48
4. 4.

   Bo stretches two strings from Q to a round balloon. QC and QD are tangent to circle O, with QC = 3x + 2 and QD = x + 14. What is x?

   6
5. 5.

   Jun stretches two strings from Q that just touch a drum. QC and QD are tangent to circle O, with QC = 4x + 1 and QD = 2x + 15. What is x?

   7
6. 6.

   Kira walks two straight paths from Q past a round pond. QC and QD are tangent to circle O, with QC = 6x − 3 and QD = 4x + 7. What is x?

   5
7. 7.

   Luz marks four points on a clock face. On circle O, chords CD and FG are equal, arc CD = 70° and arc DF = 100°. What is the measure of arc GC?

   120
8. 8.

   Milo marks four cuts on a pizza. On circle O, chords CD and FG are equal, arc CD = 50° and arc DF = 60°. What is the measure of arc GC?

   200
9. 9.

   Noah paints four dots on a plate rim. On circle O, chords CD and FG are equal, arc CD = 85° and arc DF = 110°. What is the measure of arc GC?

   80
10. 10.

    Pia places four candles on a round cake. On circle O, chords CD and FG are equal, arc CD = 40° and arc DF = 75°. What is the measure of arc GC?

    205