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Circle Theorem: Tangents from the Same Point Are the Same Length

(KS3, Year 8)

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

circle theorem tangents from same point are equal

circle theorem tangents from same point are equal

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? tangents from same point example

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.

Useful Definitions

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

circle tangent

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. tangents_from_same_point_congruent_right_triangles