Question

Construct a regular pentagon inside a circle of radius $6cm$. Suppose the pentagon is named as $ABCDE$. Then $l\left(AC\right)=?$

• A. $7cm$
• B. $9.2cm$
• C. $10.8cm$
• D. $11.4cm$

Answer 1

The correct option is D $11.4cm$

• Draw a circle of radius $r=6cm$
• Calculate the length of each side of regular polygon
• $l=2\times r\times \sin \left({180}^o/n\right),heren=5,r=6l=2\times 6\times \sin \left({36}^o\right)l=7.05cm$
• Set the compass to length $l$
• Start from any point $A$ on circle and start making arc of length $l$ until the arc touches the first point
• Join the arcs using ruler

In $△AOC,\angle AOC={72}^o\times 2={144}^o\angle OCA=\angle OAC=\frac{{180}^o-{144}^o}{2}={18}^o$

$AC=2\times r\times \cos \left(\angle OCA\right)=2\times 6\times 0.95AC=11.4cm$