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2

Part of 1998 Putnam

Problems(2)

Putnam 1998 A2

Source:

10/28/2012
Let ss be any arc of the unit circle lying entirely in the first quadrant. Let AA be the area of the region lying below ss and above the xx-axis and let BB be the area of the region lying to the right of the yy-axis and to the left of ss. Prove that A+BA+B depends only on the arc length, and not on the position, of ss.
Putnamgeometrycalculustrigonometryintegrationcollege contestsPutnam calculus
1998 Putnam B2

Source:

4/19/2013
Given a point (a,b)(a,b) with 0<b<a0<b<a, determine the minimum perimeter of a triangle with one vertex at (a,b)(a,b), one on the xx-axis, and one on the line y=xy=x. You may assume that a triangle of minimum perimeter exists.
Putnamgeometryperimetergeometric transformationreflectionanalytic geometrycollege contests