Solve Precalculus Problem: Perimeter & Area of a Pentagon

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To find the perimeter and area of a regular pentagon inscribed in a circle with a radius of 9, the problem suggests breaking the pentagon into triangles. Lines should be drawn from the center of the circle to each vertex of the pentagon to determine the angles between these lines. The angle between the lines is essential for calculating the area of the triangles formed. The discussion indicates that the user has made progress in solving the problem with community assistance. Overall, the focus is on using geometric principles to simplify the calculations for the pentagon's dimensions.
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HI guys, I'm really confusing about this Q., and I hope you guys can give me some help. :smile:

- Find the perimeter and the area of a regular pentagon inscribed in circle of radius 9.
 
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Break the inscribed pentagon into something simpler, such as triangles.
 
Draw lines from the center of the circle to the vertices of the pentagon. What is the angle between these lines?
 
I just figured out how to work on the problem. thanks everyone for helping me.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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