Question

In circle O, CD = 56, OM = 20, ON = 16 a. Find the radius. If your answer is not an integer, express it in radical form. b. Find FN. If your answer is not an integer, express it in radical form. c. Find EF. Express it as a decimal rounded to the nearest tenth.

Answer 1

a

I searched and found this figure online.

I'm guessing there's additional information that OM perpendicular to CD and EF perpendicular to ON.

The diameters meeting chords at right angles also bisect the chords, so

CM = (1/2) CD = 28

The radius OC makes the hypotenuse of a right triangle with legs OM and CM

r² = OM² + CM² = 20² + 28² = 1184

r = 4√74

a Answer: 4√74

b

FN is the leg of a right triangle with other leg ON=16 and hypotenuse OF=r because it's a radius.

FN² = r² - ON² = 1184 - 16² = 1184 - 256 = 928

FN = √928

b Answer: √928

c

EF is twice FN by the perpendicular diameter bisecting a chord theorem.

EF = 2√928

Tenths?  

c Answer: 60.9