Geometry, Student Edition
Geometry, Student Edition
1st Edition
ISBN: 9780078884849
Author: McGraw-Hill, McGraw Hill
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 11.4, Problem 1CYU
To determine

To calculate: The center, radius, an apothem and a central angle of the polygon. Also, to find the measure of the central angle

Expert Solution & Answer
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Answer to Problem 1CYU

Center is F.

Radius is FC or FD.

Apothem is FG.

Central angle is DFC.

The measure of JK is DFC=90.

Explanation of Solution

Given information: A regular hexagon is inscribed in a circle R.

Calculation:

A square is inscribed in a circle R. Therefore, the radius and the center of the circle are the radius and center of the square.

Thus, the radius and center of the square are same as that of the circle.

That is,

Center is F.

Radius is FC or FD.

It can be observed from the figure that CD is one side of the square and FG is the perpendicular that origins from the center of the square and meets the side of the square. Therefore, the segment FG is the apothem.

Apothem is FG.

The vertex of a central angle lies at the center of the polygon. The central angle is such that the sides of the angle passes through consecutive vertices of the given polygon.

The DFC fulfils all these conditions.

Hence, the central angle is DFC.

Calculate the measure of the central angle.

The given polygon is a square. Therefore, total number of sides is 4.

The measure of the central angle can be obtained by dividing 360 by the number of sides, that is, 4 in this case.

  DFC=3604=90

Thus, the measure of DFC=90.

Chapter 11 Solutions

Geometry, Student Edition

Ch. 11.1 - Prob. 2CYUCh. 11.1 - Prob. 3CYUCh. 11.1 - Prob. 4CYUCh. 11.1 - Prob. 5CYUCh. 11.1 - Prob. 6CYUCh. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9CYUCh. 11.1 - Prob. 10PPSCh. 11.1 - Prob. 11PPSCh. 11.1 - Prob. 12PPSCh. 11.1 - Prob. 13PPSCh. 11.1 - Prob. 14PPSCh. 11.1 - Prob. 15PPSCh. 11.1 - Prob. 16PPSCh. 11.1 - Prob. 17PPSCh. 11.1 - Prob. 18PPSCh. 11.1 - Prob. 19PPSCh. 11.1 - Prob. 20PPSCh. 11.1 - Prob. 21PPSCh. 11.1 - Prob. 22PPSCh. 11.1 - Prob. 23PPSCh. 11.1 - Prob. 24PPSCh. 11.1 - Prob. 25PPSCh. 11.1 - Prob. 26PPSCh. 11.1 - Prob. 27PPSCh. 11.1 - Prob. 28PPSCh. 11.1 - Prob. 29PPSCh. 11.1 - Prob. 30PPSCh. 11.1 - Prob. 31PPSCh. 11.1 - Prob. 32PPSCh. 11.1 - Prob. 33PPSCh. 11.1 - Prob. 34PPSCh. 11.1 - Prob. 35PPSCh. 11.1 - Prob. 36PPSCh. 11.1 - Prob. 37HPCh. 11.1 - Prob. 38HPCh. 11.1 - Prob. 39HPCh. 11.1 - Prob. 40HPCh. 11.1 - Prob. 41HPCh. 11.1 - Prob. 42STPCh. 11.1 - Prob. 43STPCh. 11.1 - Prob. 44STPCh. 11.1 - Prob. 45STPCh. 11.1 - Prob. 46SPRCh. 11.1 - Prob. 47SPRCh. 11.1 - Prob. 48SPRCh. 11.1 - Prob. 49SPRCh. 11.1 - Prob. 50SPRCh. 11.1 - Prob. 51SPRCh. 11.1 - Prob. 52SPRCh. 11.1 - Prob. 53SPRCh. 11.1 - Prob. 54SRCh. 11.1 - Prob. 55SRCh. 11.1 - Prob. 56SRCh. 11.1 - Prob. 57SRCh. 11.1 - Prob. 58SRCh. 11.2 - Prob. 1CYPCh. 11.2 - Prob. 2CYPCh. 11.2 - Prob. 3ACYPCh. 11.2 - Prob. 3BCYPCh. 11.2 - Prob. 4ACYPCh. 11.2 - Prob. 4BCYPCh. 11.2 - Prob. 4CCYPCh. 11.2 - Prob. 1CYUCh. 11.2 - Prob. 2CYUCh. 11.2 - Prob. 3CYUCh. 11.2 - Prob. 4CYUCh. 11.2 - Prob. 5CYUCh. 11.2 - Prob. 6CYUCh. 11.2 - Prob. 7CYUCh. 11.2 - Prob. 8PPSCh. 11.2 - Prob. 9PPSCh. 11.2 - Prob. 10PPSCh. 11.2 - Prob. 11PPSCh. 11.2 - Prob. 12PPSCh. 11.2 - Prob. 13PPSCh. 11.2 - Prob. 14PPSCh. 11.2 - Prob. 15PPSCh. 11.2 - Prob. 16PPSCh. 11.2 - Prob. 17PPSCh. 11.2 - Prob. 18PPSCh. 11.2 - Prob. 19PPSCh. 11.2 - Prob. 20PPSCh. 11.2 - Prob. 21PPSCh. 11.2 - Prob. 22PPSCh. 11.2 - Prob. 23PPSCh. 11.2 - Prob. 24PPSCh. 11.2 - Prob. 25PPSCh. 11.2 - Prob. 26PPSCh. 11.2 - Prob. 27PPSCh. 11.2 - Prob. 28PPSCh. 11.2 - Prob. 29PPSCh. 11.2 - Prob. 30PPSCh. 11.2 - Prob. 31PPSCh. 11.2 - Prob. 32PPSCh. 11.2 - Prob. 33PPSCh. 11.2 - Prob. 34PPSCh. 11.2 - Prob. 35HPCh. 11.2 - Prob. 36HPCh. 11.2 - Prob. 37HPCh. 11.2 - Prob. 38HPCh. 11.2 - Prob. 39STPCh. 11.2 - Prob. 40STPCh. 11.2 - Prob. 41STPCh. 11.2 - Prob. 42STPCh. 11.2 - Prob. 43SPRCh. 11.2 - Prob. 44SPRCh. 11.2 - Prob. 45SPRCh. 11.2 - Prob. 46SPRCh. 11.2 - Prob. 47SPRCh. 11.2 - Prob. 48SPRCh. 11.2 - Prob. 49SPRCh. 11.2 - Prob. 50SPRCh. 11.2 - Prob. 51SPRCh. 11.2 - Prob. 52SPRCh. 11.2 - Prob. 53SRCh. 11.2 - Prob. 54SRCh. 11.2 - Prob. 55SRCh. 11.3 - Prob. 1CYPCh. 11.3 - Prob. 2CYPCh. 11.3 - Prob. 3ACYPCh. 11.3 - Prob. 3BCYPCh. 11.3 - Prob. 3CCYPCh. 11.3 - Prob. 3DCYPCh. 11.3 - Prob. 1CYUCh. 11.3 - Prob. 2CYUCh. 11.3 - Prob. 3CYUCh. 11.3 - Prob. 4CYUCh. 11.3 - Prob. 5CYUCh. 11.3 - Prob. 6CYUCh. 11.3 - Prob. 7CYUCh. 11.3 - Prob. 8PPSCh. 11.3 - Prob. 9PPSCh. 11.3 - Prob. 10PPSCh. 11.3 - Prob. 11PPSCh. 11.3 - Prob. 12PPSCh. 11.3 - Prob. 13PPSCh. 11.3 - Prob. 14PPSCh. 11.3 - Prob. 15PPSCh. 11.3 - Prob. 16PPSCh. 11.3 - Prob. 17PPSCh. 11.3 - Prob. 18PPSCh. 11.3 - Prob. 19PPSCh. 11.3 - Prob. 20PPSCh. 11.3 - Prob. 21PPSCh. 11.3 - Prob. 22PPSCh. 11.3 - Prob. 23PPSCh. 11.3 - Prob. 24PPSCh. 11.3 - Prob. 25PPSCh. 11.3 - Prob. 26PPSCh. 11.3 - Prob. 27PPSCh. 11.3 - Prob. 28PPSCh. 11.3 - Prob. 29PPSCh. 11.3 - Prob. 30PPSCh. 11.3 - Prob. 31PPSCh. 11.3 - Prob. 32PPSCh. 11.3 - Prob. 33PPSCh. 11.3 - Prob. 34PPSCh. 11.3 - Prob. 35PPSCh. 11.3 - Prob. 36PPSCh. 11.3 - Prob. 37PPSCh. 11.3 - Prob. 38PPSCh. 11.3 - Prob. 39PPSCh. 11.3 - Prob. 40PPSCh. 11.3 - Prob. 41PPSCh. 11.3 - Prob. 42PPSCh. 11.3 - Prob. 43PPSCh. 11.3 - Prob. 44HPCh. 11.3 - Prob. 45HPCh. 11.3 - Prob. 46HPCh. 11.3 - Prob. 47HPCh. 11.3 - Prob. 48HPCh. 11.3 - Prob. 49HPCh. 11.3 - Prob. 50STPCh. 11.3 - Prob. 51STPCh. 11.3 - Prob. 52STPCh. 11.3 - Prob. 53STPCh. 11.3 - Prob. 54SPRCh. 11.3 - Prob. 55SPRCh. 11.3 - Prob. 56SPRCh. 11.3 - Prob. 57SPRCh. 11.3 - Prob. 58SPRCh. 11.3 - Prob. 59SRCh. 11.3 - Prob. 60SRCh. 11.3 - Prob. 61SRCh. 11.4 - Prob. 1CYPCh. 11.4 - Prob. 2CYPCh. 11.4 - Prob. 3ACYPCh. 11.4 - Prob. 3BCYPCh. 11.4 - Prob. 3CCYPCh. 11.4 - Prob. 4ACYPCh. 11.4 - Prob. 4BCYPCh. 11.4 - Prob. 5ACYPCh. 11.4 - Prob. 5BCYPCh. 11.4 - Prob. 1CYUCh. 11.4 - Prob. 2CYUCh. 11.4 - Prob. 3CYUCh. 11.4 - Prob. 4CYUCh. 11.4 - Prob. 5CYUCh. 11.4 - Prob. 6CYUCh. 11.4 - Prob. 7CYUCh. 11.4 - Prob. 8PPSCh. 11.4 - Prob. 9PPSCh. 11.4 - Prob. 10PPSCh. 11.4 - Prob. 11PPSCh. 11.4 - Prob. 12PPSCh. 11.4 - Prob. 13PPSCh. 11.4 - Prob. 14PPSCh. 11.4 - Prob. 15PPSCh. 11.4 - Prob. 16PPSCh. 11.4 - Prob. 17PPSCh. 11.4 - Prob. 18PPSCh. 11.4 - Prob. 19PPSCh. 11.4 - Prob. 20PPSCh. 11.4 - Prob. 21PPSCh. 11.4 - Prob. 22PPSCh. 11.4 - Prob. 23PPSCh. 11.4 - Prob. 24PPSCh. 11.4 - Prob. 25PPSCh. 11.4 - Prob. 26PPSCh. 11.4 - Prob. 27PPSCh. 11.4 - Prob. 28PPSCh. 11.4 - Prob. 29PPSCh. 11.4 - Prob. 30PPSCh. 11.4 - Prob. 31PPSCh. 11.4 - Prob. 32PPSCh. 11.4 - Prob. 33PPSCh. 11.4 - Prob. 34PPSCh. 11.4 - Prob. 35HPCh. 11.4 - Prob. 36HPCh. 11.4 - Prob. 37HPCh. 11.4 - Prob. 38HPCh. 11.4 - Prob. 39HPCh. 11.4 - Prob. 40STPCh. 11.4 - Prob. 41STPCh. 11.4 - Prob. 42STPCh. 11.4 - Prob. 43STPCh. 11.4 - Prob. 44SPRCh. 11.4 - Prob. 45SPRCh. 11.4 - Prob. 46SPRCh. 11.4 - Prob. 47SPRCh. 11.4 - Prob. 48SPRCh. 11.4 - Prob. 49SPRCh. 11.4 - Prob. 50SPRCh. 11.4 - Prob. 51SPRCh. 11.4 - Prob. 52SPRCh. 11.4 - Prob. 53SPRCh. 11.4 - Prob. 54SRCh. 11.4 - Prob. 55SRCh. 11.5 - Prob. 1ACYPCh. 11.5 - Prob. 1BCYPCh. 11.5 - Prob. 2ACYPCh. 11.5 - Prob. 2BCYPCh. 11.5 - Prob. 3CYPCh. 11.5 - Prob. 1CYUCh. 11.5 - Prob. 2CYUCh. 11.5 - Prob. 3CYUCh. 11.5 - Prob. 4CYUCh. 11.5 - Prob. 5CYUCh. 11.5 - Prob. 6PPSCh. 11.5 - Prob. 7PPSCh. 11.5 - Prob. 8PPSCh. 11.5 - Prob. 9PPSCh. 11.5 - Prob. 10PPSCh. 11.5 - Prob. 11PPSCh. 11.5 - Prob. 12PPSCh. 11.5 - Prob. 13PPSCh. 11.5 - Prob. 14PPSCh. 11.5 - Prob. 15PPSCh. 11.5 - Prob. 16PPSCh. 11.5 - Prob. 17PPSCh. 11.5 - Prob. 18PPSCh. 11.5 - Prob. 19PPSCh. 11.5 - Prob. 20PPSCh. 11.5 - Prob. 21PPSCh. 11.5 - Prob. 22PPSCh. 11.5 - Prob. 23PPSCh. 11.5 - Prob. 24PPSCh. 11.5 - Prob. 25HPCh. 11.5 - Prob. 26HPCh. 11.5 - Prob. 27HPCh. 11.5 - Prob. 28HPCh. 11.5 - Prob. 29HPCh. 11.5 - Prob. 30STPCh. 11.5 - Prob. 31STPCh. 11.5 - Prob. 32STPCh. 11.5 - Prob. 33STPCh. 11.5 - Prob. 34SPRCh. 11.5 - Prob. 35SPRCh. 11.5 - Prob. 36SPRCh. 11.5 - Prob. 37SPRCh. 11.5 - Prob. 38SPRCh. 11.5 - Prob. 39SPRCh. 11.5 - Prob. 40SPRCh. 11.5 - Prob. 41SPRCh. 11.5 - Prob. 42SRCh. 11.5 - Prob. 43SRCh. 11.5 - Prob. 44SRCh. 11.5 - Prob. 45SRCh. 11 - Prob. 1GRFCCh. 11 - Prob. 2GRFCCh. 11 - Prob. 3GRFCCh. 11 - Prob. 4GRFCCh. 11 - Prob. 5GRFCCh. 11 - Prob. 6GRFCCh. 11 - Prob. 7GRFCCh. 11 - Prob. 8GRFCCh. 11 - Prob. 9GRFCCh. 11 - Prob. 10GRFCCh. 11 - Prob. 11GRFCCh. 11 - Prob. 12GRFCCh. 11 - Prob. 13GRFCCh. 11 - Prob. 14GRFCCh. 11 - Prob. 1MCQCh. 11 - Prob. 2MCQCh. 11 - Prob. 3MCQCh. 11 - Prob. 4MCQCh. 11 - Prob. 5MCQCh. 11 - Prob. 6MCQCh. 11 - Prob. 7MCQCh. 11 - Prob. 8MCQCh. 11 - Prob. 9MCQCh. 11 - Prob. 10MCQCh. 11 - Prob. 11MCQCh. 11 - Prob. 12MCQCh. 11 - Prob. 13MCQCh. 11 - Prob. 14MCQCh. 11 - Prob. 15MCQCh. 11 - Prob. 16MCQCh. 11 - Prob. 17MCQCh. 11 - Prob. 18MCQCh. 11 - Prob. 19MCQCh. 11 - Prob. 20MCQCh. 11 - Prob. 1SGRCh. 11 - Prob. 2SGRCh. 11 - Prob. 3SGRCh. 11 - Prob. 4SGRCh. 11 - Prob. 5SGRCh. 11 - Prob. 6SGRCh. 11 - Prob. 7SGRCh. 11 - Prob. 8SGRCh. 11 - Prob. 9SGRCh. 11 - Prob. 10SGRCh. 11 - Prob. 11SGRCh. 11 - Prob. 12SGRCh. 11 - Prob. 13SGRCh. 11 - Prob. 14SGRCh. 11 - Prob. 15SGRCh. 11 - Prob. 16SGRCh. 11 - Prob. 17SGRCh. 11 - Prob. 18SGRCh. 11 - Prob. 19SGRCh. 11 - Prob. 20SGRCh. 11 - Prob. 21SGRCh. 11 - Prob. 22SGRCh. 11 - Prob. 23SGRCh. 11 - Prob. 24SGRCh. 11 - Prob. 25SGRCh. 11 - Prob. 26SGRCh. 11 - Prob. 27SGRCh. 11 - Prob. 28SGRCh. 11 - Prob. 29SGRCh. 11 - Prob. 30SGRCh. 11 - Prob. 31SGRCh. 11 - Prob. 32SGRCh. 11 - Prob. 33SGRCh. 11 - Prob. 34SGRCh. 11 - Prob. 35SGRCh. 11 - Prob. 1PTCh. 11 - Prob. 2PTCh. 11 - Prob. 3PTCh. 11 - Prob. 4PTCh. 11 - Prob. 5PTCh. 11 - Prob. 6PTCh. 11 - Prob. 7PTCh. 11 - Prob. 8PTCh. 11 - Prob. 9PTCh. 11 - Prob. 10PTCh. 11 - Prob. 11PTCh. 11 - Prob. 12PTCh. 11 - Prob. 13PTCh. 11 - Prob. 14PTCh. 11 - Prob. 15PTCh. 11 - Prob. 16PTCh. 11 - Prob. 17PTCh. 11 - Prob. 18PTCh. 11 - Prob. 19PTCh. 11 - Prob. 20PTCh. 11 - Prob. 1PSTCh. 11 - Prob. 2PSTCh. 11 - Prob. 1STPCh. 11 - Prob. 2STPCh. 11 - Prob. 3STPCh. 11 - Prob. 4STPCh. 11 - Prob. 5STPCh. 11 - Prob. 6STPCh. 11 - Prob. 7STPCh. 11 - Prob. 8STPCh. 11 - Prob. 9STPCh. 11 - Prob. 10STPCh. 11 - Prob. 11STPCh. 11 - Prob. 12STP
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