The center of the polygon lies at the Radius of the 5 units.
What is polygon?
Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
JKLMN is a regular polygon inscribed in a circle.
Since, its a regular polygon,
JN = NM = 5.88 units
"Perpendicular drawn from the center of the circle to any chord is the bisector of the chord"
Therefore, PQ will be the perpendicular bisector of chord NM.
[tex]QM = \dfrac{1}{2}(NM)[/tex]
[tex]QM = =\dfrac{1}{2}\times 5.88[/tex]
QM = 2.94 units
By applying Pythagoras theorem in ΔPQM,
PM² = PQ² + QM²
PM² = (4.05)² + (2.94)²
[tex]PM = \sqrt{16.4025+8.6936}[/tex]
[tex]PM =\sqrt{25.0461}[/tex]
PM = 5 units
Therefore, radius of the circle is 5 units.
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