# What are the tangent properties in a circle? Please help, I find them very confusing.

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### 1 Answer

**One important property of a tangent to a circle is that the radius of the circle is perpendicular to tangent to circle at the point of tangency**.

This property helps you to prove following important property of tangent to a circle, such that: **the tangent segments to a circle, from an external point are equal.**

You may prove this property using the previous property that states that the radii of a circle are perpendicular to the tangent segments.

Considering the circle `C` , of center `O` ,the radii `OA, OB` , the external point `C` and the tangent segments `CA, CB` , you may prove that the right angle triangles `OAC` and `OBC` are congruent, hence, by definition, the tangent segments `CA` and `CB` are also congruent.

The statement that the right triangles `OAC` and `OBC` are congruent is valid, with respect to the following aspects, such that:

- `OA = OB` (legs of triangles `OAC` and `OBC` that are the radii of circle)

-` hat(AOC) = hat(BOC) = 90^o`

- `OC = OC` (common leg in triangles)

Since you have two equal lengths and the angle comprised also equal, you may state that the right triangles `OAC` and `OBC` are congruent, hence `CA = CB` .