Circle arc segment

A circle with a radius r=8 cm is divided by points K and L in a ratio of 5 to 4. Calculate the sizes of the center and circumferential angles, corresponding to both arcs and the area of the larger segment.

Final Answer:

A =  200 °
B =  160 °
S₁ =  111.7011 cm²

Step-by-step explanation:

$$\begin{gathered} A+B=360 \\ A=5/4\cdot B \\ A=\frac{5}{4+5}\cdot 360=200^{\circ } \end{gathered}$$

$B=360-A=360-200=160^{\circ }$

$$\begin{gathered} r=8\text{cm} \\ {S}_1=\frac{A}{360}\cdot \pi \cdot r^2=\frac{200}{360}\cdot 3.1416\cdot 8^2=111.7011{\text{cm}}^2 \end{gathered}$$

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