Therefore we can draw a line connecting those points of tangency.

We are now at the point of tangency.

The two line segments connecting opposite points of tangency have equal length.

The slope increases until the line reaches a point of tangency with the total product curve.

The two points of tangency are also double points.

Draw a horizontal line through that point of tangency and find its intersection with the vertical line.

Repeating this same argument with the other two points of tangency completes the proof of the result.

To the right of the point of tangency the firm is using too little capital and diminishing returns to labor are causing costs to increase.

That point of tangency is the Feuerbach point of the triangle.

A line connecting all points of tangency between the indifference curve and the budget constraint is called the expansion path.

The intersections of that circle with the intersecting given lines are the two points of tangency.

The same reciprocal relation exists between a point P outside the circle and the secant line joining its two points of tangency.

Hence, the points of tangency between the transformed circles lie on a line midway between the two parallel lines.

The more usual solution will lie in the non-zero interior at the point of tangency between the objective function and the constraint.

Their points of tangency with the nine-point circle form a triangle, the Feuerbach triangle.

The lines perpendicular to the tangents to a circle at the points of tangency are concurrent at the center.

The point of tangency travels around the deltoid twice while each end travels around it once.

The investor's optimal portfolio is found at the point of tangency of the efficient frontier with the indifference curve.

Again make sure that the entity selections are made near the point of tangency and point of perpendicularity, respectively.

A parabola meets it at only one point, but it is a point of tangency and therefore counts twice.

The geometry was eventually defined using combinations of circular arcs, transitioning at points of tangency.

In bringing the chisel into contact with the revolving surface, the mathematical principle of the "point of tangency" is illustrated.

The complexity enters when calculating intersections at points of tangency and intersections along positive dimensional sets.

For each point p, construct the stereographic projection of s(p) with p as the point of tangency.

The inscribed circle meets the triangle in three points of tangency, forming an equilateral contact triangle with side length where is the golden ratio.