Answer:
Length of arc BC is 14 centimeter.
Step-by-step explanation:
Point A, B and C lie on a circle with center Q.
The area of sector AQB is twice the area of sector BQC.
[tex]\text{Area of sector AQB}=2\text{Area of sector BQC}[/tex]
[tex]\text{Formula for area of sector:} =\frac{\theta}{360^{\circ}}\times \pi r^2[/tex]
Let sector AQB subtended angle [tex]\theta_1[/tex] at centre.
Let sector BQC subtended angle [tex]\theta_2[/tex] at centre.
[tex]\therefore \frac{\theta_1}{360^{\circ}}\times \pi r^2=2\times \frac{\theta_2}{360^{\circ}}\times \pi r^2[/tex]
[tex]\theta_1=2\theta_2[/tex]
[tex]\text{Formula for Length of arc:} =\frac{\theta}{360^{\circ}}\times 2\pi r[/tex]
Length of arc AB is 28 centimeters.
[tex]\text{Formula for Length of arc AB} =\frac{\theta_1}{360^{\circ}}\times 2\pi r[/tex]
[tex]\frac{\theta_1}{360^{\circ}}\times 2\pi r=28--------------(1)[/tex]
Length of arc BC is l centimeters.
[tex]\frac{\theta_2}{360^{\circ}}\times 2\pi r=l----------------(2)[/tex]
Divide equation 1 by equation 2 and we get
[tex]\dfrac{\theta_1}{\theta_2}=\dfrac{28}{l}[/tex]
[tex]\dfrac{2\theta_2}{\theta_2}=\dfrac{28}{l}[/tex] [tex]\because \theta_1=2\theta_2[/tex]
[tex]l=\frac{28}{2}\Rightarrow 14\text{ centimeter}[/tex]
Thus, Length of arc BC is 14 centimeter.
