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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Two tangent segments drawn from a common external point to the same circle are congruent.

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If $AB$ and $AC$ are tangent segments to $⊙O,$ then $AB≅AC.$

Consider two triangles.

- The triangle formed by the radius $OB,$ the segment $OA,$ and the tangent segment $AB.$
- The triangle formed by the radius $OC,$ the segment $OA,$ and the tangent segment $AC.$

These two triangles can be visualized in the diagram.

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Note that $B$ and $C$ are points of tangency. Therefore, by the Tangent to Circle Theorem, $∠B$ and $∠C$ are right angles. Consequently, $△ABO$ and $△ACO$ are right triangles.

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Because all radii of the same circle are congruent, it can be said that $OB$ and $OC$ are congruent. Moreover, $△ABO$ and $△ACO$ share the same hypotenuse $OA.$ By the Reflexive Property of Congruence, $OA$ is congruent to itself.

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Combining all of this information, it can be said that the hypotenuse and one leg of $△ABO$ are congruent to the hypotenuse and the corresponding leg of $△ACO.$

$OB≅OCOA≅OA $

Therefore, by the Hypotenuse-Leg Theorem, $△ABO$ and $△ACO$ are congruent triangles. Since corresponding parts of congruent figures are congruent, it can be said that $AB$ and $AC$ are congruent.

$AB≅AC$