Chords and tangents: lengths and right angles

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Ren fits a round sticker snugly inside a triangle frame. The circle touches all three sides of △CDF. What is the perimeter of △CDF, in cm?

   24
2. 2.

   Tala draws a circle touching all three sides of a paper triangle. The circle touches all three sides of △CDF. What is the perimeter of △CDF, in cm?

   30
3. 3.

   Zee fits a round window inside a triangle frame. The circle touches all three sides of △CDF. What is the perimeter of △CDF, in cm?

   36
4. 4.

   Ari cuts a triangle sandwich around a round slice of cucumber. The circle touches all three sides of △CDF. What is the perimeter of △CDF, in cm?

   34
5. 5.

   Jun pulls a chain from Q to a round gear. QC is tangent to circle O at C, and line QO meets the circle first at D. What is the radius, in cm?

   8
6. 6.

   Kira lays a straw from Q to a round tray. QC is tangent to circle O at C, and line QO meets the circle first at D. What is the radius, in cm?

   10
7. 7.

   Luz ties two kite strings from Q that just touch a round balloon. QC and QD are tangent to circle O at C and D, and ∠CQD = 50°. What is ∠COD, in degrees?

   130
8. 8.

   Milo draws two chain lines from Q around a gear. QC and QD are tangent to circle O at C and D, and ∠CQD = 78°. What is ∠COD, in degrees?

   102
9. 9.

   Noah walks two straight paths from Q that just touch a round pond. QC and QD are tangent to circle O at C and D, and ∠CQD = 34°. What is ∠COD, in degrees?

   146
10. 10.

    Pia stretches two strings from Q that just touch a drum. QC and QD are tangent to circle O at C and D, and ∠CQD = 57°. What is ∠COD, in degrees?

    123