Walking through a circle

Geometry Level 2

When I walk to classes on my campus I have to go through a roundabout and I wondered if it would be shorter to take the path which goes to the center of the circle then to the other edge or to walk the circumference. At what angle θ \theta (in degrees) is the distance to walk from the point on the circumference of the circle to the center then another point on the circumference equal to the arc length between the two points?


The answer is 114.592.

Andrew Majors by Andrew Majors , 20, USA

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1 solution

Andrew Majors
Oct 20, 2018

Sorry I dunno what happened but the answer should be 114.592. I don’t know how it ended up as 360 anyways I got this through the following. \text{Sorry I dunno what happened but the answer should be 114.592. I don't know how it ended up as 360 anyways I got this through the following.} 2 r = θ 360 × 2 π r 1 = θ 360 × π 1 θ = π 360 θ = 360 π θ = 114.592 \begin{aligned} \ 2r = \frac {\theta }{ 360} \times 2 \pi r\\ \ 1= \frac{\theta} {360} \times \pi\\ \ \frac {1}{\theta} = \frac{\pi}{360}\\ \ \theta= \frac{360} {\pi}\\ \ \theta=114.592\\ \end{aligned}

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In order to change the question, simply tag a Brilliant moderator such as @Brilliant Mathematics

Blan Morrison - 2 years, 7 months ago

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How do I tag a moderator? Do I just do it in a comment like you did

Andrew Majors - 2 years, 7 months ago

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Yes. Type "@" and then start typing their name.

Blan Morrison - 2 years, 7 months ago

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