Circle Theorem: Tangents from the Same Point Are the Same Length
(KS3, Year 8)

The Lesson

Two tangents drawn from the same point outside of the circle are the same length and form two congruent right triangles.

How to Use the Circle Theorem where Tangents from the Same Point Are the Same Length

Question

The tangent OA is 10 cm in length. What is the length of the tangent OB?

Step-by-Step:

1

Tangents drawn from the same point outside of the circle have the same length.
OB = OA = 10 cm

Answer:

The tangent OB has length 10 cm.

Lesson Slides

The slider below shows a real example of the circle theorem where tangents from the same point are equal. Open the slider in a new tab

Useful Definitions

A tangent is a line that touches the circle at one point.

Tangents from the Same Point Form Right Congruent Triangles

Congruent triangles are the same shape. The corresponding sides and angles are the same. The tangents from the same point form congruent right triangles with the radii to the tangents and the line halfway between the tangents.

The two right triangles have the same angles and side lengths as each other.
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See Also

What is a right triangle? What is a radius? What is a circle? What are the circle theorems?