Circle Theorem: Tangents from the Same Point Are Equal (Mathematics Lesson)
Circle Theorem: Tangents from the Same Point Are EqualTwo 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 EqualQuestion: 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 TrianglesThe 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 EqualThe slider below shows a real example of the circle theorem that tangents from the same point are equal:
NoteWHAT 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 THEOREMSCircle 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 DEFINITIONSA 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.