+576 a. Construct a radius from C to O. Since CD=44 and OM is a right angle to the chord it bisects the chord, ergo CM=22. We can use the pythagorean theorem to find CO.
22^2+20^2=CO^2
CO=sqrt(884) which is about 29.7
+576 b. To find FNwe construct the radius from O to F and recall that its length is sqrt(884). Then apply the pythagorean theorem to the new triangle
19^2+FN^2 =(sqrt(884))^2
361+FN^2=884
FN^2=523
FN=sqrt(523)
+128656 a)
Since OM is perpendicular to CD, it also bisects it. Then CM = 22. And we can find radius CO thusly..
CM^2 + OM^2 = CO^2
22^2 + 20^2 = CO^2
884 = CO^2 take the square root of both sides
√884 = CO = 2√221
b)
OF^2 - ON^2 = FN^2 .....but OF = CO (since both are radii)
CO^2 - ON^2 = FN^2
884 - 19^2 = FN^2
884 - 361 = FN^2
523 = FN^2 take square root of both sides
√523 = FN
c) Since ON is perpendicular to EF it bisects it.....and FN = √523....so EF = 2√523 = 45.7
