Question

The radius of a circle is 20 cm with chord AC = 12 cm. Determine the measure of .

Answer 1

Using the cosine rule formula to solve for angle O

`\begin{gathered} 12^2=20^2+20^2-2(20)(20)cosO \\ \end{gathered}`

Solve for angle O

`\begin{gathered} 144=400+400-800cosO \\ 800cosO=800-144 \\ cosO=(656)/(800)=0.82 \\ O=\cos^(-1)(0.82)=34.92^(\circ\:) \\ \therefore O=34.92^0 \end{gathered}`

Therefore,

`\begin{gathered} \angle AOC=2\angle ABC \\ \therefore\angle ABC=(\angle AOC)/(2)=(34.92)/(2)=17.46^0 \end{gathered}`

Hence, the answer is

`\angle ABC=17.46^0`