Tangency

In this section we will apply the concept of connectedness in dimension d to study tangencies of algebraic varieties.

To be tangent to a circle or arc, a line must touch the circle or arc at only one point, and a line drawn from the center of the circle or arc must be perpendicular to the tangent line at the point of tangency. (See Figure 6.82.)

If the original tangency is at A, then the new tangency cannot be at O or P, as either possibility would require two indifference curves to cross.[…]Instead, the new tangency is at a point like B.