Tangents — O/L Mathematics

How do I practise Tangents?

1 question with a worked solution

1. PT is a tangent drawn from an external point P to a circle at point of contact T. If O is the centre of the circle, radius OT = 5 cm, and OP = 13 cm, find the length of the tangent PT.
   1. A) 10 cm
   2. B) 14 cm
   3. C) 8 cm
   4. D) 12 cm
   Check my answer

   Correct answer: D) 12 cm

   By theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact (angle OTP = 90°). In right triangle OTP: PT² + OT² = OP² → PT² + 5² = 13² → PT² + 25 = 169 → PT² = 144 → PT = 12 cm.

   Show worked solution

   Step 1: State tangent-radius theorem: Radius OT is perpendicular to tangent PT at point T, so triangle OTP is right-angled at T. Step 2: Hypotenuse is OP = 13 cm, leg OT = 5 cm. Step 3: By Pythagoras' theorem: PT = √(OP² - OT²) = √(13² - 5²) = √(169 - 25) = √144 = 12 cm. Answer: 12 cm.
   Modelled on: the O/L Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Tangents fit in the syllabus?

Grade 11 · Term 3