Tangents, Radii and the Alternate Segment Theorem · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Tangents and the alternate segment

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. Two tangents from point P touch a circle at A and B. Each tangent is 7 cm and chord AB is 5 cm. What is the perimeter of triangle PAB in cm?

    Answer: ______________

  2. A tangent meets a radius at the point of contact. What is that angle?

    • 45 degrees
    • 180 degrees
    • 90 degrees
    • 60 degrees

  3. A tangent meets a radius at the point of contact. What is that angle?

    • 45 degrees
    • 90 degrees
    • 60 degrees

  4. Two tangents from P touch a circle at A and B. Each tangent is 7 cm and chord AB is 5 cm. What is the perimeter of triangle PAB in cm?

    Answer: ______________

  5. Centre O, point of contact T, outside point P. OT = 5 cm, OP = 13 cm. How long is tangent TP in cm?

    Answer: ______________

  6. Tangents from P are 9 cm each. Triangle PQB has PB 9 and QB 12, right-angled at B. What is PQ?

    • 21
    • 15
    • 18

  7. Tangent at T with chord TC makes 50 degrees. The angle in the opposite arc is x. What is x?

    • 100 degrees
    • 130 degrees
    • 40 degrees
    • 50 degrees

  8. Priya says the two tangents from one outside point are always equal. Is Priya right?

    Circle one:   True   False

  9. Chord AB subtends 30 degrees in the opposite arc. A tangent at A makes angle y with AB. What is y?

    • 30 degrees
    • 60 degrees
    • 90 degrees

  10. A tangent and chord meet at 64 degrees, so the opposite arc angle at T is also 64 degrees. Triangle RST has angle R = 50 degrees and angle T = 64 degrees. What is angle S in degrees?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_Y-Xf0BOb1C-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Tangents and the alternate segment W1-mt_Y-Xf0BOb1C-s1

  1. 19 · Equal tangents give 7 + 7 + 5 = 19.
  2. 90 degrees · Radius meets tangent at a right angle. The 180 option confuses it with a straight line.
  3. 90 degrees · Radius meets tangent at a right angle.
  4. 19 · Equal tangents give 7 plus 7 plus 5, which is 19.
  5. 12 · Root of 169 minus 25 = 12.
  6. 15 · Root of 81 plus 144 is 15.
  7. 50 degrees · Alternate segment copies it across: 50. The 130 option uses a supplementary mix up.
  8. True · Symmetry about the centre line forces the pair to match.
  9. 30 degrees · Alternate segment: y equals the opposite arc angle, 30.
  10. 66 · Angles total 180: 180 minus 64 minus 50 = 66.
Worksheet · LightMySky