Chords and tangents: lengths and right angles

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Ren draws a straight path that just touches a round pond at C. Line QC is tangent to circle O at C, and ∠COQ = 52°. What is ∠CQO, in degrees?

   38
2. 2.

   Tala draws a bike chain leaving a round gear at C. Line QC is tangent to circle O at C, and ∠COQ = 64°. What is ∠CQO, in degrees?

   26
3. 3.

   Zee pulls a string tight so it just touches a drum at C. Line QC is tangent to circle O at C, and ∠COQ = 40°. What is ∠CQO, in degrees?

   50
4. 4.

   Ari rolls a play ball against a straight wall at C. Line QC is tangent to circle O at C, and ∠COQ = 76°. What is ∠CQO, in degrees?

   14
5. 5.

   Bo draws a round pond on a map, with a bench at Q. QC is tangent to circle O at C. How long is QC, in cm?

   40
6. 6.

   Esme draws a chain from Q to a round gear. QC is tangent to circle O at C. How long is QC, in cm?

   30
7. 7.

   Kira lays a straw from Q to just touch a round plate. QC is tangent to circle O at C. How long is QC, in cm?

   36
8. 8.

   Luz cuts a straight chord across a round pizza. Chord CF = 18 cm. Radius OD crosses CF at H at a right angle, and CH = (2x + 1) cm. What is x?

   4
9. 9.

   Noah cuts a straight line across a round cake. Chord CF = 30 cm. Radius OD crosses CF at H at a right angle, and CH = (x + 6) cm. What is x?

   9
10. 10.

    Pia draws a stripe of icing across a round cookie. Chord CF = 16 cm. Radius OD crosses CF at H at a right angle, and CH = (2x − 2) cm. What is x?

    5