Question

What is the radius of polygon JKLMN ?

Answer 1

Answer:

Radius of the circle is 5 units.

Step-by-step explanation:

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.

QM = $\frac{1}{2}(NM)$

QM = $\frac{1}{2}(5.88)$

QM = 2.94 units

By applying Pythagoras theorem in ΔPQM,

PM² = PQ² + QM²

PM² = (4.05)² + (2.94)²

PM = $\sqrt{16.4025+8.6436}$

PM = $\sqrt{25.0461}$

PM = 5 units

Therefore, radius of the circle is 5 units.