Theorem 12-3
Intersecting Tangents (on the exterior)
Include Formula
Short Definition
When two tangents are drawn to a circle from an external point, they intersect at a point which is equally distant from that point and the center of the circle.
Formula: If two tangents are drawn to a circle from an external point P, then the tangents intersect at a point X which is equidistant to P and the center O of the circle. This can be expressed as OP = OX.
Theorem 12-3 states that if two tangents are drawn to a circle from an exterior point, then the segments they form are congruent.
Formula:
If two tangents are drawn from an exterior point P to a circle with center O, then PA = PB, where A and B are the points of contact of the tangents and PA and PB are the lengths of the segments.