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Circle Theorem: Tangents from the Same Point Are Equal (Mathematics Lesson)

Circle Theorem: Tangents from the Same Point Are Equal

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 that Tangents From the Same Point Are Equal

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



Tangents drawn from the same point outside of the circle have the same length.

OB = OA = 10cm

The tangent OB has length 10cm

Tangents From the Same Point Form Congruent Triangles

The tangents 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.

A Real Example of How to Use the Circle Theorem that Tangents from the Same Point Are Equal

The slider below shows a real example of the circle theorem that tangents from the same point are equal:
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Note
WHAT IS A CIRCLE?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

CIRCLE THEOREMS

Circle theorems relate to the angles and lines within circles.

Two tangents drawn from the same point outside of the circle are the same length and form two congruent right triangles is one of the circle theorems. There are several others.

Read more about circle theorems

USEFUL DEFINITIONS

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



Congruent triangles are the same shape. The corresponding sides and angles are the same.