Skills · Geometry · Circles

Tangents, chords and secants

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. chords AB and CD meeting at E: AE 10, EB ?, CE 5, ED 14ABCDE10?514
    Chords AB and CD meet at E. Find the length marked ?.
  2. circle O, PA and PB tangent at A and B: PA ?, PB 29OPAB?29
    PA and PB are tangent to the circle. Find the length marked ?.
  3. circle O, PA and PB tangent at A and B: PA ?, PB 6OPAB?6
    PA and PB are tangent to the circle. Find the length marked ?.
  4. circle O, PA tangent at A: OA 20, PA ?, OP 29OAP20?29
    PA is tangent to the circle at A. Find the length marked ?.
  5. circle O, PA tangent at A: OA 36, PA ?, OP 45OAP36?45
    PA is tangent to the circle at A. Find the length marked ?.
  6. chords AB and CD meeting at E: AE 10, EB 4, CE ?, ED 8ABCDE104?8
    Chords AB and CD meet at E. Find the length marked ?.
  7. circle O, PA and PB tangent at A and B: PA ?, PB 28OPAB?28
    PA and PB are tangent to the circle. Find the length marked ?.
  8. circle O, PA tangent at A: OA ?, PA 4, OP 5OAP?45
    PA is tangent to the circle at A. Find the length marked ?.

Answer key

  1. 7 units
  2. 29 units
  3. 6 units
  4. 21 units
  5. 27 units
  6. 5 units
  7. 28 units
  8. 3 units

Sample Sheet · Level 3

  1. circle O, PA and PB tangent at A and B: PA x + 14, PB 3x − 14OPABx + 143x − 14
    PA and PB are tangent to the circle. Find PA.
  2. tangent PT and secant PAB: PT x + 3, PA 4, AB 5PABTx + 345
    PT is tangent to the circle at T. Find PT.
  3. circle O, PA and PB tangent at A and B: PA x + 11, PB 3x − 19OPABx + 113x − 19
    PA and PB are tangent to the circle. Find PB.
  4. circle O, PA tangent at A: OA 20, PA x + 1, OP 29OAP20x + 129
    PA is tangent to the circle at A. Find PA.
  5. chords AB and CD meeting at E: AE 5x − 18, EB 6, CE x + 12, ED 4ABCDE5x − 186x + 124
    Chords AB and CD meet at E. Find AE.
  6. circle O, PA tangent at A: OA 6, PA x + 2, OP 10OAP6x + 210
    PA is tangent to the circle at A. Find PA.
  7. chords AB and CD meeting at E: AE 8, EB x + 5, CE 4x + 4, ED 4ABCDE8x + 54x + 44
    Chords AB and CD meet at E. Find CE.
  8. tangent PT and secant PAB: PT x + 1, PA 9, AB 16PABTx + 1916
    PT is tangent to the circle at T. Find PT.

Answer key

  1. 28 units
  2. 6 units
  3. 26 units
  4. 21 units
  5. 12 units
  6. 8 units
  7. 16 units
  8. 15 units

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Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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