Graphed in the standard (x, y) coordinate plane below is the line I and the circle with equation (x-2)2 +y2 = 1. Line i passes through (0,0) and is tangent to circle A and B is the center of the circle. What is the measure of AOB

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

1260=3*6*7*10=3^2*2^2*7*5 perfect cude = 3^3*2^

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