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Tangent segment theorem means that the lenghts of the two tangent to a same circle drawn from an external point are equal. The theorem is as follows. Angle PAC and Angle PBC =90° (This is also a theorem. Tangents are perpendicular to radius and they are 90°) In right angled triangle PAC and right angled triangle PBC, Segment CA is congruent to segment CB, (radius of the same circle) Hypotenuse PC is congruent to Hypotenuse PC,(common side of both the triangles mentioned above) Therefore, triangle PAC is congruent to triangle PBC, (Hypotenuse side test) Therefore, segment PA is congruent to segment PB, (corresponding sides of congruent trianglesl Therefore, PA=PB. If you don't understand anything please feel free to ask more questions. Picture attached.
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In the picture, segment AC and segment BC are not joined. But you have to join it, otherwise it will be difficult to understand this theorem. 
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