| 21. | A line joining tangency points of isoquants and isocosts ( with input prices held constant ) is called the expansion path.
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| 22. | As " n " increases the order of self intersection increases : transverse crossing, ordinary tangency, etc.
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| 23. | The blue and red circles swell to tangency, and are inverted in the grey circle, producing two straight lines.
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| 24. | The sides of the black triangle are perpendiculars to the lines through the tangencies and the center of the red circle.
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| 25. | Since it preserves tangencies, angles and circles, inversion transforms one Steiner chain into another of the same number of circles.
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| 26. | The more usual solution will lie in the non-zero interior at the point of tangency between the objective function and the constraint.
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| 27. | On the one hand you call it " for visualization ", but then it is also the sign in terms of these tangencies.
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| 28. | Their point of tangency is chosen as the center of inversion in a circle that intersects each of the two touching circles in two places.
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| 29. | Since tangencies and circles are preserved under inversion, this property of all tangencies lying on a circle is also true in the original chain.
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| 30. | Since tangencies and circles are preserved under inversion, this property of all tangencies lying on a circle is also true in the original chain.
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