Two Tangents from a Point (Cambridge (CIE) IGCSE International Maths)

Revision Note

Written by: Naomi C

Reviewed by: Dan Finlay

Two Tangents from a Point

Circle Theorem: Tangents from an external point are equal in length

Two tangents from the same external point are equal in length
This means that a kite can be formed by two tangents meeting a circle
- The kite below has a vertical line of symmetry
  - It is formed from two congruent triangles back-to-back
- The kite will have two right angles where the tangents meet the radii
  - You can use Pythagoras and SOHCAHTOA on each of these triangles

A circle with centre, O, and two points on the circumference, R and S. Tangents to the circle at these two points, intersect at a point outside the circle, T. OR and OS are radii. ROST forms a kite.

Examiner Tips and Tricks

Look for tangents in the exam and draw on the radius at right angles to see if it helps

Worked Example

Consider the diagram below.

A circle with centre, O, and two points on the circumference, S and R. Tangents to the circle, at S and R, meet at a point outside the circle, T. OR = 3 cm, OT = 11 cm.

(a) Find the length ST.

The lines ST and RT are both tangents to the circle
They meet the two radii on the circumference at the points S and T

Angle TSO = 90° because a radius and a tangent meet at right angles

Use Pythagoras' theorem on the right-angled triangle OST to calculate the length ST

$\begin{array}{rcl} 3^{2} + {(S T)}^{2} & = & 11^{2} \\ 9 + {(S T)}^{2} & = & 121 \\ {(S T)}^{2} & = & 112 \\ S T & = & \sqrt{112} = 10.58300 . . . \end{array}$

ST = 10.6 cm (3 s.f.)

(b) Find the length RT.

Two tangents from the same external point are equal in length

ST = RT

RT = 10.6 cm (3 s.f.)

Last updated: 26 June 2024

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Previous:Tangent & RadiusNext:Perimeter