MathDB

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Part of 2011 JHMT

Problems(1)

2011 JHMT Geometry #1

Source:

9/5/2023
Let Dx,yD_{x,y} denote the half-disk of radius 11 with its curved boundary externally tangent to the unit circle at the point (x,y)(x, y), such that the straight boundary of the disk is parallel to the tangent line (so the point of tangency is the middle of the curved boundary). Find the area of the union of the Dx,yD_{x,y} over all (x,y)(x, y) with x2+y2=1x^2 + y^2 = 1 (that is, (x,y)(x,y) is on the unit circle).
geometry