In circle O CD 44 OM 20 ON 19 CD OM EF ON The figure is no

In circle O, CD = 44. OM = 20. ON= 19, CD OM, EF ON (The figure is not drawn to scale.) Show your work. Find the radius. If your answer is not an integer, express it in radical form. Find FN. If your answer is not an integer, express it in radical form. Find EF. Express it as a decimal rounded to the nearest tenth.

Solution

a. CO is radius. Given CD is perpendicular to OM, and O is center, by the law of perpendilar bisector in circle, CM = MD

So, CD=44. Therefore, CM=MD=44

OM = 20

CO = sqrt(20^2 +22^2) = sqrt( 400+484) = 29.732

b. Similarly,
CO=OE=radius = 29.732
So, EN =FN= sqrt(884-361) = 22.87

c) Hence, EF = 2*FN = 2*22.87 = 45.74