# star inscribed in a circle

Printable View

• Feb 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.

Please help me solve this.I need the answer asap.
• Feb 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.

Please help me solve this.I need the answer asap.

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