A chord

In a circle of radius 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the cord at the center of the circle
Hence find the length of the minor arc cut off by the chord.

Correct answer:

α =  120 °
l =  12.5664 cm

Step-by-step explanation:

$$\begin{gathered} r=6\text{cm} \\ d=3\text{cm} \\ \cos \alpha /2=d:r \\ \phi =2\cdot \arccos (d/r)=2\cdot \arccos (3/6)\doteq 2.0944\text{rad} \\ \alpha =\phi \to \text{°}=\phi \cdot \frac{180}{\pi }\text{°}=2.0944\cdot \frac{180}{\pi }\text{°}=120\text{°}=120^{\circ } \end{gathered}$$

$l=\phi \cdot r=2.0944\cdot 6=12.5664\text{cm}$

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