Segment lengths from chords, secants and tangents

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Noah ties strings from Q to a round balloon. QC and QG are tangent to circle O; a secant from Q passes through D and F. How long is QG, in cm?

   6
2. 2.

   Pia draws chain lines from Q to a big gear. QC and QG are tangent to circle O; a secant from Q passes through D and F. How long is QG, in cm?

   30
3. 3.

   Ren maps two paths from Q past a round pond. QC and QG are tangent to circle O; a secant from Q passes through D and F. How long is QG, in cm?

   20
4. 4.

   Tala stretches strings from Q to a drum. QC and QG are tangent to circle O; a secant from Q passes through D and F. How long is QG, in cm?

   10
5. 5.

   Ari draws two crossing chords on a clock. Chords CF and DG of circle O cross at H; CH = x cm and HF = (x + 3) cm. What is x?

   5
6. 6.

   Bo ices two crossing lines on a cookie. Chords CF and DG of circle O cross at H; CH = x cm and HF = (x + 4) cm. What is x?

   6
7. 7.

   Esme sews two crossing stripes on a rug. Chords CF and DG of circle O cross at H; CH = x cm and HF = (x + 5) cm. What is x?

   3
8. 8.

   Jun maps a round pond and a bench at Q. QC is tangent to circle O, and a secant from Q passes through D and F. How long is QD, in cm?

   16
9. 9.

   Kira draws lines from Q to a big gear. QC is tangent to circle O, and a secant from Q passes through D and F. How long is QD, in cm?

   20
10. 10.

    Milo lays straws from Q across a round tray. QC is tangent to circle O, and a secant from Q passes through D and F. How long is QD, in cm?

    12