Segment lengths from chords, secants and tangents

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Noah maps two paths from Q across a round pond. Secants QCD and QGF meet at Q, outside circle O. How long is GF, the part inside the circle, in cm?

   11
2. 2.

   Pia cuts two lines from Q across a pizza. Secants QCD and QGF meet at Q, outside circle O. How long is GF, the part inside the circle, in cm?

   8
3. 3.

   Ren draws two lines from Q across a clock. Secants QCD and QGF meet at Q, outside circle O. How long is GF, the part inside the circle, in cm?

   13
4. 4.

   Tala lays two strings from Q across a rug. Secants QCD and QGF meet at Q, outside circle O. How long is GF, the part inside the circle, in cm?

   7
5. 5.

   Zee 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 DF, in cm?

   21
6. 6.

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

   7
7. 7.

   Bo stretches strings from Q to a big drum. QC is tangent to circle O, and a secant from Q passes through D and F. How long is DF, in cm?

   42
8. 8.

   Esme 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 DF, in cm?

   24
9. 9.

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

   12
10. 10.

    Milo sews two crossing stripes on a rug. Chords CF and DG of circle O cross at H; CH = (x + 4) cm. What is x?

    5