A chord

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

Final 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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