Grade 10 · Math · Geometry

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

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Chords and tangents: lengths and right angles

Grade 10 Math Worksheet - Challenge Me

NameDate

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

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?
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?
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?
Esme holds a string at Q beside a drum. QC is tangent to circle O at C, and line QO meets the circle first at D. What is the radius, in cm?
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?
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?
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?
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?
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?
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?

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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