Weaved Circle Perimeter

Geometry Level 1

If each unit circle passes through the centers of the other 2 circles, what is the perimeter?

Do not include the parts that are contained within the figure.

3 π 3 \pi 4 π 4 \pi 5 π 5 \pi 6 π 6 \pi

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Chung Kevin by Chung Kevin , 46, Australia

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2 solutions

3 Helpful 1 Interesting 1 Brilliant 0 Confused

Yea! That's the way I did it too.

Chung Kevin - 4 years, 6 months ago
Hana Wehbi
Jul 2, 2016

If I draw a triangle whose vertices are the three points of intersection of the three circles. Its side is 2 2 , which the same as the length of the diameter of each circle. This tells us that the part of the circle we need to calculate its perimeter is half the total of the unit circle. The perimter of the part that we need from each circle is 2 π / 2 = π 2\pi/2 =\pi . Thus, the total perimeter is 3 × π = 3 π 3 \times \pi= 3\pi

2 Helpful 0 Interesting 0 Brilliant 0 Confused

How the length of sides of triangle is 2?

Apurv Singh - 4 years, 7 months ago

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If we draw the tangent to two circles, is going to be a side of our triangle. Also, it is the diameter of the third circle which is =2, since each circle has a radius of 1. Each circle is a unit circle.

Hana Wehbi - 4 years, 7 months ago

Nice solution, @Hana Nakkache Just using the Euclidean method of constructing an equilateral triangle gives you the same result, but I think that's what you were saying.

Drex Beckman - 4 years, 11 months ago

Thank you.

Hana Wehbi - 4 years, 11 months ago

How did you know the length of sides of triangle ?

Prince Raj - 4 years, 7 months ago

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If we draw the tangent to two circles, is going to be a side of our triangle. Also, it is the diameter of the third circle which is =2, since each circle has a radius of 1. Each circle is a unit circle.

Hana Wehbi - 4 years, 7 months ago

@Hana Nakkache or rather how do you know that each side of the triangle constructed will be 2 units?

Nathanael Raj - 4 years, 6 months ago

How do you know a line from 2 points of intersection will pass through the centre of the circle?

Nathanael Raj - 4 years, 6 months ago

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it says in the problem each unit circle passes through the centers of the other two circles.

Hana Wehbi - 4 years, 6 months ago

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