A regular pentagon has sides of 10 cm. Find the radius of the largest circle which can be drawn inside the pentagon.

Panoptik asked Apr 18, 2022

299,715 views

36 votes

A regular pentagon has sides of 10 cm. Find the radius of the largest circle which can

be drawn inside the pentagon.

Panoptik asked Apr 18, 2022

2.8k points

Your comment on this question:

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Email me at this address if my answer is selected or commented on:Email me if my answer is selected or commented on

Privacy: Your email address will only be used for sending these notifications.

24 votes

Answer is 6.88 cm

Divide the pentagon radially into five congruent, isosceles triangles. Each triangle has a vertex angle of 360°÷5=72° and altitude of 5÷tan(36°).

radius of circle = 5÷tan(36°) = 6.88 cm

3.0k points

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

1.6m questions

2.0m answers