Circumferential 8399

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.

Correct answer:

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

Step-by-step explanation:

A+B = 360
A = 5/4·B

A+B = 360
4A-5B = 0

Pivot: Row 1 ↔ Row 2
4A-5B = 0
A+B = 360

Row 2 - 1/4 · Row 1 → Row 2
4A-5B = 0
2.25B = 360


B = 360/2.25 = 160
A = 0+5B/4 = 0+5 · 160/4 = 200

A = 200
B = 160

Our linear equations calculator calculates it.

$B=160=160^{\circ }$

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

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