# star inscribed in a circle

• February 23rd 2009, 04:15 AM
hven191
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.

• February 23rd 2009, 05:27 AM
earboth
Quote:

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.
• February 25th 2009, 12:34 AM
hven191
Thanks for the help earboth! It really helped me a lot! (Happy)