Grade 10 · Math · Geometry

10th grade Segment lengths from chords, secants and tangents worksheet

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Segment lengths from chords, secants and tangents

Grade 10 Math Worksheet - Challenge Me

NameDate

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

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?
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?
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?
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?
Zee cuts two crossing lines on a pizza. Chords CF and DG of circle O cross at H; CH = x cm and HF = (x + 2) cm. What is x?
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?
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?
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?
Luz stretches strings from Q to a drum. QC is tangent to circle O, and a secant from Q passes through D and F. How long is QD, in cm?
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?

Segment lengths from chords, secants and tangents. Every version has 10 questions, and the answer key prints on the second page.

Standard: G-C.A.2

segment: A straight piece of a line with two ends.

secant segment: From an outside point Q through the circle to the far side.

outside piece: The part of a secant from Q to the circle.

whole secant: The outside piece plus the piece inside the circle.

tangent segment: From Q to the point where the tangent touches.

Your child made the sums of the chord pieces equal instead of the products.

Your child multiplied a piece of one chord by a piece of the other.

Your child doubled the tangent length instead of multiplying it by itself.

Ask: two chords cross; do the pieces add up the same, or multiply the same?

Ask: which two pieces make up chord CF?

Ask: what does QC² mean?

What is the most common mistake with segment lengths from chords, secants and tangents?

Your child made the sums of the chord pieces equal instead of the products.

How can I help my child with segment lengths from chords, secants and tangents?

Ask: two chords cross; do the pieces add up the same, or multiply the same?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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