Condition for Two Circles to Have a Common Tangent at an Intersection Point

Condition for Two Circles to Have a Common Tangent at an Intersection Point

If two circles intersect at $$p$$, their common tangent at $$p$$ exists only when their tangent directions at $$p$$ coincide.

$$O_1P\parallel O_2P$$

Usage

- Used to identify tangency rather than ordinary intersection between two circles.