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Tangents and Secants Examples

Example 1

Suppose line m intersects ⊙X at point Z and m is perpendicular to XZ. What is the maximum number of other points on ⊙X that m can intersect?

Example 2

Is there a maximum number of secant lines two circles can have in common? If so, what is it? (In other words, given two circles, how many lines m can you draw so that m is a secant of both circles?)

Example 3

In the figure below, segments CA and CB are tangent to ⊙O at points A and B, respectively. If OA = 8 cm and AC = 18 cm, what is the length of BC?