11. Each straight line segment is an tangency between the given isoquant and one of the cost curves. 12. The points having the minimum vertical separation are also the tangency points for the maximally separated parallel tangents. 13. If intersects in only one point, then it is a tangent line and is the point of tangency . 14. The set of all such tangency points is called the firm's " expansion path ". 15. A line connecting all points of tangency between the indifference curve and the budget constraint is called the expansion path. 16. The relationship between transversality and tangency is clearest when \ ell _ 1 + \ ell _ 2 = m. 17. Hence, the points of tangency between the transformed circles lie on a line midway between the two parallel lines. 18. In M�bius geometry, tangency between a line and a circle becomes a special case of tangency between two circles. 19. In M�bius geometry, tangency between a line and a circle becomes a special case of tangency between two circles. 20. The investor's optimal portfolio is found at the point of tangency of the efficient frontier with the indifference curve.
