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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` .
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