Question

why will a inscribed circle will only work within a regular polygon.

Answer 1

http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1042&context=mathmidexppap&sei-redir=1&referer=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dwhy%2520will%2520a%2520inscribed%2520circle%2520will%2520only%2520work%2520within%2520a%2520regular%2520polygon.%26source%3Dweb%26cd%3D1%26ved%3D0CCUQFjAA%26url%3Dhttp%253A%252F%252Fdigitalcommons.unl.edu%252Fcgi%252Fviewcontent.cgi%253Farticle%253D1042%2526context%253Dmathmidexppap%26ei%3DYI57T6yYH6Tg2AW1yeCCDg%26usg%3DAFQjCNHl9vkGMG8j9OUJLp8HXRF08VZBFA#search=%22why%20will%20inscribed%20circle%20will%20only%20work%20within%20regular%20polygon.%22

Answer 2

that should help you

Answer 3

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to each of its congruent sides. A circle inscribed in a regular polygon has radius equal to the apothem. The inscribed circle is tangent to the sides of the polygon.