To calculate: The center, radius, an apothem and a central
Answer to Problem 1CYP
Center is
Radius is
Apothem is
Central angle is
The measure of JK is
Explanation of Solution
Given information: A regular hexagon is inscribed in a
Calculation:
A regular hexagon is inscribed in a circle R. Therefore, the radius and the center of the circle are the radius and center of the hexagon.
Thus, the radius and center of the hexagon are same as that of the circle.
That is,
Center is
Radius is
It can be observed from the figure that KL is one side of the hexagon and RS is the perpendicular that origins from the center of the hexagon and meets the side of the hexagon. Therefore, the segment
Apothem is
The vertex of a central angle lies at the center of the hexagon. The central angle is such that the sides of the angle passes through consecutive vertices of the given hexagon.
The
Hence, the central angle is
Calculate the measure of the central angle.
The given polygon is a hexagon. Therefore, total number of sides is 6.
The measure of the central angle can be obtained by dividing
Thus, the measure of
Chapter 11 Solutions
Geometry, Student Edition
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