# Thread: star inscribed in a circle

1. ## star inscribed in a circle

I am trying to answer this problem as a practice for an exam and I can't seem to find the correct answer.

In a circle with a diameter of 10m, a regular five pointed star touching its circumference is inscribed.What is the area of the part not covered by the star.

2. Originally Posted by hven191
I am trying to answer this problem as a practice for an exam and I can't seem to find the correct answer.

In a circle with a diameter of 10m, a regular five pointed star touching its circumference is inscribed.What is the area of the part not covered by the star.

Do you mean a pentagram? (See attachment)

The radius is divided into 2 parts by an inner vertex:

$\dfrac{red}{blue} = \dfrac{blue}{red+blue}$

which is nothing but the golden ratio.

3. Thanks for the help earboth! It really helped me a lot!

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# area of a star inscribed in a circle

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