Thank you for visiting In each circle below a 50 angle with a vertex at the center of the circle is drawn How are minor arc lengths CD and. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The arc lengths are proportional: Arc CD = 4 arc EF.
Given that,
Circle A and B are shown.
Line segments DA and CA are radii with lengths of 8 centimeters.
Angle DAC is 50 degrees.
Line segments FB and EB are radii with lengths of 2 centimeters.
Angle FBE is 50 degrees.
In each circle below, a 50° angle with a vertex at the center of the circle is drawn.
We have to determine,
How are minor arc lengths CD and EF related?
According to the question,
The length of an arc that subtends an angle of θ degrees at the center of the circle is given by,
[tex]\rm Length = \dfrac{\theta}{360} \times 2\pi r[/tex]
Line segments DA and CA are radii with lengths of 8 centimeters.
[tex]\rm Length \ of \ CD= \dfrac{50}{360} \times 2\pi \times 8\\\\\[/tex]
Line segments FB and EB are radii with lengths of 2 centimeters
[tex]\rm Length \ of \ EF= \dfrac{50}{360} \times 2\pi \times 2\\\\[/tex]
On comparing both the lengths
[tex]\rm\dfrac{ Length \ of \ CD }{Length \ of \ EF}= \dfrac{\dfrac{50}{360} \times 8\pi \times 2}{ \dfrac{50}{360} \times 2\pi \times 2\\\\}\\\\\dfrac{ Length \ of \ CD }{Length \ of \ EF} = \dfrac{4}{1}\\\\Length \ of \ CD }{}=4\times Length \ of \ EF[/tex]
Hence, The arc lengths are proportional: Arc CD = 4 arc EF.
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