Grade 10 · Math · Geometry

10th grade Chords and tangents: lengths and right angles worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Chords and tangents: lengths and right angles

Grade 10 Math Worksheet - Building Confidence

NameDate

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

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?
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?
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?
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?
Jun stretches a string from Q to just touch a drum. QC is tangent to circle O at C. How long is QC, in cm?
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?
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?
Milo draws a chord across a clock face. Chord CF = 26 cm. Radius OD crosses CF at H at a right angle, and CH = (2x + 3) cm. What is x?
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?
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?

Chords and tangents: lengths and right angles. Every version has 10 questions, and the answer key prints on the second page.

Standard: G-C.A.2

chord: A segment joining two points on the circle.

tangent: A line that touches the circle at exactly one point.

point of tangency: The point where the tangent touches the circle.

perpendicular (⊥): Meeting at a right angle, 90°.

inscribed circle: A circle inside a triangle touching all three sides.

Your child forgot that a tangent meets the radius at a right angle.

Your child split the angles evenly, as if two sides were equal.

Your child subtracted two side lengths of a right triangle instead of using the squares on the sides.

Ask: what angle does the radius make with the tangent line where they touch?

Ask: which angle in this triangle do we already know because of the tangent?

Ask: what rule connects the three sides of a right triangle?

What is the most common mistake with chords and tangents: lengths and right angles?

Your child forgot that a tangent meets the radius at a right angle.

How can I help my child with chords and tangents: lengths and right angles?

Ask: what angle does the radius make with the tangent line where they touch?

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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