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 12.7, Problem 3ACYP
To determine

To check whether the given postulate of plane Euclidean geometry has a corresponding statement in spherical geometry.

Expert Solution & Answer
Check Mark

Answer to Problem 3ACYP

For spherical geometry, ‘Arcs on a great circle are the shortest path between two paths’

Explanation of Solution

Given information: A line segment is the shortest path between two points.

Formula used:

Great circle: A plane can intersect a sphere in a point or in a circle. If the circle contains the center of the sphere, the intersection is called a great circle.. The endpoints of a diameter of a great circle are called poles

In spherical geometry the ‘line segment’ refers to arcs of great circle.

Therefore, as in plane geometry, a ‘line segment’ on a sphere is the shortest ‘line’ connecting two points.

Therefore, a corresponding statement of‘A line segment is the shortest path between two points’ for spherical geometry is ‘Arcs on a great circle are the shortest path between two path’, which is called minor arcof great circle.

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Chapter 12 Solutions

Geometry, Student Edition

Ch. 12.1 - Prob. 1CYPCh. 12.1 - Prob. 2CYPCh. 12.1 - Prob. 3CYPCh. 12.1 - Prob. 1CYUCh. 12.1 - Prob. 2CYUCh. 12.1 - Prob. 3CYUCh. 12.1 - Prob. 4CYUCh. 12.1 - Prob. 5CYUCh. 12.1 - Prob. 6CYUCh. 12.1 - Prob. 7CYU
Ch. 12.1 - Prob. 8PPSCh. 12.1 - Prob. 9PPSCh. 12.1 - Prob. 10PPSCh. 12.1 - Prob. 11PPSCh. 12.1 - Prob. 12PPSCh. 12.1 - Prob. 13PPSCh. 12.1 - Prob. 14PPSCh. 12.1 - Prob. 15PPSCh. 12.1 - Prob. 16PPSCh. 12.1 - Prob. 17PPSCh. 12.1 - Prob. 18PPSCh. 12.1 - Prob. 19PPSCh. 12.1 - Prob. 20PPSCh. 12.1 - Prob. 21PPSCh. 12.1 - Prob. 22PPSCh. 12.1 - Prob. 23PPSCh. 12.1 - Prob. 24PPSCh. 12.1 - Prob. 25PPSCh. 12.1 - Prob. 26PPSCh. 12.1 - Prob. 27PPSCh. 12.1 - Prob. 28PPSCh. 12.1 - Prob. 29PPSCh. 12.1 - Prob. 30PPSCh. 12.1 - Prob. 31PPSCh. 12.1 - Prob. 32PPSCh. 12.1 - Prob. 33PPSCh. 12.1 - Prob. 34PPSCh. 12.1 - Prob. 35HPCh. 12.1 - Prob. 36HPCh. 12.1 - Prob. 37HPCh. 12.1 - Prob. 38HPCh. 12.1 - Prob. 39HPCh. 12.1 - Prob. 40STPCh. 12.1 - Prob. 41STPCh. 12.1 - Prob. 42STPCh. 12.1 - Prob. 43STPCh. 12.1 - Prob. 44SPRCh. 12.1 - Prob. 45SPRCh. 12.1 - Prob. 46SPRCh. 12.1 - Prob. 47SPRCh. 12.1 - Prob. 48SRCh. 12.1 - Prob. 49SRCh. 12.1 - Prob. 50SRCh. 12.2 - Prob. 1CYPCh. 12.2 - Prob. 2CYPCh. 12.2 - Prob. 3ACYPCh. 12.2 - Prob. 3BCYPCh. 12.2 - Prob. 4CYPCh. 12.2 - Prob. 1CYUCh. 12.2 - Prob. 2CYUCh. 12.2 - Prob. 3CYUCh. 12.2 - Prob. 4CYUCh. 12.2 - Prob. 5CYUCh. 12.2 - Prob. 6CYUCh. 12.2 - Prob. 7CYUCh. 12.2 - Prob. 8CYUCh. 12.2 - Prob. 9PPSCh. 12.2 - Prob. 10PPSCh. 12.2 - Prob. 11PPSCh. 12.2 - Prob. 12PPSCh. 12.2 - Prob. 13PPSCh. 12.2 - Prob. 14PPSCh. 12.2 - Prob. 15PPSCh. 12.2 - Prob. 16PPSCh. 12.2 - Prob. 17PPSCh. 12.2 - Prob. 18PPSCh. 12.2 - Prob. 19PPSCh. 12.2 - Prob. 20PPSCh. 12.2 - Prob. 21PPSCh. 12.2 - Prob. 22PPSCh. 12.2 - Prob. 23PPSCh. 12.2 - Prob. 24PPSCh. 12.2 - Prob. 25PPSCh. 12.2 - Prob. 26PPSCh. 12.2 - Prob. 27PPSCh. 12.2 - Prob. 28PPSCh. 12.2 - Prob. 29PPSCh. 12.2 - Prob. 30PPSCh. 12.2 - Prob. 31PPSCh. 12.2 - Prob. 32PPSCh. 12.2 - Prob. 33PPSCh. 12.2 - Prob. 34PPSCh. 12.2 - Prob. 35PPSCh. 12.2 - Prob. 36PPSCh. 12.2 - Prob. 37PPSCh. 12.2 - Prob. 38PPSCh. 12.2 - Prob. 39HPCh. 12.2 - Prob. 40HPCh. 12.2 - Prob. 41HPCh. 12.2 - Prob. 42HPCh. 12.2 - Prob. 43HPCh. 12.2 - Prob. 44HPCh. 12.2 - Prob. 45STPCh. 12.2 - Prob. 46STPCh. 12.2 - Prob. 47STPCh. 12.2 - Prob. 48STPCh. 12.2 - Prob. 49SPRCh. 12.2 - Prob. 50SPRCh. 12.2 - Prob. 51SPRCh. 12.2 - Prob. 52SPRCh. 12.2 - Prob. 53SPRCh. 12.2 - Prob. 54SRCh. 12.2 - Prob. 55SRCh. 12.2 - Prob. 56SRCh. 12.3 - Prob. 1CYPCh. 12.3 - Prob. 2ACYPCh. 12.3 - Prob. 2BCYPCh. 12.3 - Prob. 3ACYPCh. 12.3 - Prob. 3BCYPCh. 12.3 - Prob. 4CYPCh. 12.3 - Prob. 5ACYPCh. 12.3 - Prob. 5BCYPCh. 12.3 - Prob. 1CYUCh. 12.3 - Prob. 2CYUCh. 12.3 - Prob. 3CYUCh. 12.3 - Prob. 4CYUCh. 12.3 - Prob. 5CYUCh. 12.3 - Prob. 6CYUCh. 12.3 - Prob. 7PPSCh. 12.3 - Prob. 8PPSCh. 12.3 - Prob. 9PPSCh. 12.3 - Prob. 10PPSCh. 12.3 - Prob. 11PPSCh. 12.3 - Prob. 12PPSCh. 12.3 - Prob. 13PPSCh. 12.3 - Prob. 14PPSCh. 12.3 - Prob. 15PPSCh. 12.3 - Prob. 16PPSCh. 12.3 - Prob. 17PPSCh. 12.3 - Prob. 18PPSCh. 12.3 - Prob. 19PPSCh. 12.3 - Prob. 20PPSCh. 12.3 - Prob. 21PPSCh. 12.3 - Prob. 22PPSCh. 12.3 - Prob. 23PPSCh. 12.3 - Prob. 24PPSCh. 12.3 - Prob. 25PPSCh. 12.3 - Prob. 26PPSCh. 12.3 - Prob. 27PPSCh. 12.3 - Prob. 28PPSCh. 12.3 - Prob. 29PPSCh. 12.3 - Prob. 30PPSCh. 12.3 - Prob. 31PPSCh. 12.3 - Prob. 32PPSCh. 12.3 - Prob. 33PPSCh. 12.3 - Prob. 34PPSCh. 12.3 - Prob. 35PPSCh. 12.3 - Prob. 36PPSCh. 12.3 - Prob. 37HPCh. 12.3 - Prob. 38HPCh. 12.3 - Prob. 39HPCh. 12.3 - Prob. 40HPCh. 12.3 - Prob. 41HPCh. 12.3 - Prob. 42HPCh. 12.3 - Prob. 43STPCh. 12.3 - Prob. 44STPCh. 12.3 - Prob. 45STPCh. 12.3 - Prob. 46SPRCh. 12.3 - Prob. 47SPRCh. 12.3 - Prob. 48SPRCh. 12.3 - Prob. 49SPRCh. 12.3 - Prob. 50SPRCh. 12.3 - Prob. 51SPRCh. 12.3 - Prob. 52SPRCh. 12.3 - Prob. 53SPRCh. 12.3 - Prob. 54SPRCh. 12.3 - Prob. 55SRCh. 12.3 - Prob. 56SRCh. 12.3 - Prob. 57SRCh. 12.4 - Prob. 1ACYPCh. 12.4 - Prob. 1BCYPCh. 12.4 - Prob. 2ACYPCh. 12.4 - Prob. 2BCYPCh. 12.4 - Prob. 3CYPCh. 12.4 - Prob. 4CYPCh. 12.4 - Prob. 1CYUCh. 12.4 - Prob. 2CYUCh. 12.4 - Prob. 3CYUCh. 12.4 - Prob. 4CYUCh. 12.4 - Prob. 5CYUCh. 12.4 - Prob. 6CYUCh. 12.4 - Prob. 7CYUCh. 12.4 - Prob. 8CYUCh. 12.4 - Prob. 9CYUCh. 12.4 - Prob. 10PPSCh. 12.4 - Prob. 11PPSCh. 12.4 - Prob. 12PPSCh. 12.4 - Prob. 13PPSCh. 12.4 - Prob. 14PPSCh. 12.4 - Prob. 15PPSCh. 12.4 - Prob. 16PPSCh. 12.4 - Prob. 17PPSCh. 12.4 - Prob. 18PPSCh. 12.4 - Prob. 19PPSCh. 12.4 - Prob. 20PPSCh. 12.4 - Prob. 21PPSCh. 12.4 - Prob. 22PPSCh. 12.4 - Prob. 23PPSCh. 12.4 - Prob. 24PPSCh. 12.4 - Prob. 25PPSCh. 12.4 - Prob. 26PPSCh. 12.4 - Prob. 27PPSCh. 12.4 - Prob. 28PPSCh. 12.4 - Prob. 29PPSCh. 12.4 - Prob. 30PPSCh. 12.4 - Prob. 31PPSCh. 12.4 - Prob. 32PPSCh. 12.4 - Prob. 33PPSCh. 12.4 - Prob. 34PPSCh. 12.4 - Prob. 35PPSCh. 12.4 - Prob. 36PPSCh. 12.4 - Prob. 37PPSCh. 12.4 - Prob. 38PPSCh. 12.4 - Prob. 39PPSCh. 12.4 - Prob. 40PPSCh. 12.4 - Prob. 41PPSCh. 12.4 - Prob. 42HPCh. 12.4 - Prob. 43HPCh. 12.4 - Prob. 44HPCh. 12.4 - Prob. 45HPCh. 12.4 - Prob. 46HPCh. 12.4 - Prob. 47HPCh. 12.4 - Prob. 48STPCh. 12.4 - Prob. 49STPCh. 12.4 - Prob. 50STPCh. 12.4 - Prob. 51STPCh. 12.4 - Prob. 52SPRCh. 12.4 - Prob. 53SPRCh. 12.4 - Prob. 54SPRCh. 12.4 - Prob. 55SPRCh. 12.4 - Prob. 56SPRCh. 12.4 - Prob. 57SPRCh. 12.4 - Prob. 58SPRCh. 12.4 - Prob. 59SPRCh. 12.4 - Prob. 60SRCh. 12.4 - Prob. 61SRCh. 12.4 - Prob. 62SRCh. 12.5 - Prob. 1ACYPCh. 12.5 - Prob. 1BCYPCh. 12.5 - Prob. 2ACYPCh. 12.5 - Prob. 2BCYPCh. 12.5 - Prob. 2CCYPCh. 12.5 - Prob. 3CYPCh. 12.5 - Prob. 1CYUCh. 12.5 - Prob. 2CYUCh. 12.5 - Prob. 3CYUCh. 12.5 - Prob. 4CYUCh. 12.5 - Prob. 5CYUCh. 12.5 - Prob. 6CYUCh. 12.5 - Prob. 7CYUCh. 12.5 - Prob. 8CYUCh. 12.5 - Prob. 9CYUCh. 12.5 - Prob. 10PPSCh. 12.5 - Prob. 11PPSCh. 12.5 - Prob. 12PPSCh. 12.5 - Prob. 13PPSCh. 12.5 - Prob. 14PPSCh. 12.5 - Prob. 15PPSCh. 12.5 - Prob. 16PPSCh. 12.5 - Prob. 17PPSCh. 12.5 - Prob. 18PPSCh. 12.5 - Prob. 19PPSCh. 12.5 - Prob. 20PPSCh. 12.5 - Prob. 21PPSCh. 12.5 - Prob. 22PPSCh. 12.5 - Prob. 23PPSCh. 12.5 - Prob. 24PPSCh. 12.5 - Prob. 25PPSCh. 12.5 - Prob. 26PPSCh. 12.5 - Prob. 27PPSCh. 12.5 - Prob. 28PPSCh. 12.5 - Prob. 29PPSCh. 12.5 - Prob. 30PPSCh. 12.5 - Prob. 31PPSCh. 12.5 - Prob. 32PPSCh. 12.5 - Prob. 33PPSCh. 12.5 - Prob. 34PPSCh. 12.5 - Prob. 35PPSCh. 12.5 - Prob. 36HPCh. 12.5 - Prob. 37HPCh. 12.5 - Prob. 38HPCh. 12.5 - Prob. 39HPCh. 12.5 - Prob. 40HPCh. 12.5 - Prob. 41STPCh. 12.5 - Prob. 42STPCh. 12.5 - Prob. 43STPCh. 12.5 - Prob. 44STPCh. 12.5 - Prob. 45SPRCh. 12.5 - Prob. 46SPRCh. 12.5 - Prob. 47SPRCh. 12.5 - Prob. 48SPRCh. 12.5 - Prob. 49SRCh. 12.5 - Prob. 50SRCh. 12.5 - Prob. 51SRCh. 12.5 - Prob. 52SRCh. 12.6 - Prob. 1ACYPCh. 12.6 - Prob. 1BCYPCh. 12.6 - Prob. 2ACYPCh. 12.6 - Prob. 2BCYPCh. 12.6 - Prob. 2CCYPCh. 12.6 - Prob. 3ACYPCh. 12.6 - Prob. 3BCYPCh. 12.6 - Prob. 4CYPCh. 12.6 - Prob. 1CYUCh. 12.6 - Prob. 2CYUCh. 12.6 - Prob. 3CYUCh. 12.6 - Prob. 4CYUCh. 12.6 - Prob. 5CYUCh. 12.6 - Prob. 6CYUCh. 12.6 - Prob. 7CYUCh. 12.6 - Prob. 8CYUCh. 12.6 - Prob. 9CYUCh. 12.6 - Prob. 10PPSCh. 12.6 - Prob. 11PPSCh. 12.6 - Prob. 12PPSCh. 12.6 - Prob. 13PPSCh. 12.6 - Prob. 14PPSCh. 12.6 - Prob. 15PPSCh. 12.6 - Prob. 16PPSCh. 12.6 - Prob. 17PPSCh. 12.6 - Prob. 18PPSCh. 12.6 - Prob. 19PPSCh. 12.6 - Prob. 20PPSCh. 12.6 - Prob. 21PPSCh. 12.6 - Prob. 22PPSCh. 12.6 - Prob. 23PPSCh. 12.6 - Prob. 24PPSCh. 12.6 - Prob. 25PPSCh. 12.6 - Prob. 26PPSCh. 12.6 - Prob. 27PPSCh. 12.6 - Prob. 28PPSCh. 12.6 - Prob. 29PPSCh. 12.6 - Prob. 30PPSCh. 12.6 - Prob. 31PPSCh. 12.6 - Prob. 32PPSCh. 12.6 - Prob. 33PPSCh. 12.6 - Prob. 34PPSCh. 12.6 - Prob. 35PPSCh. 12.6 - Prob. 36PPSCh. 12.6 - Prob. 37PPSCh. 12.6 - Prob. 38PPSCh. 12.6 - Prob. 39PPSCh. 12.6 - Prob. 40PPSCh. 12.6 - Prob. 41PPSCh. 12.6 - Prob. 42PPSCh. 12.6 - Prob. 43PPSCh. 12.6 - Prob. 44PPSCh. 12.6 - Prob. 45HPCh. 12.6 - Prob. 46HPCh. 12.6 - Prob. 47HPCh. 12.6 - Prob. 48HPCh. 12.6 - Prob. 49STPCh. 12.6 - Prob. 50STPCh. 12.6 - Prob. 51STPCh. 12.6 - Prob. 52STPCh. 12.6 - Prob. 53SPRCh. 12.6 - Prob. 54SPRCh. 12.6 - Prob. 55SPRCh. 12.6 - Prob. 56SPRCh. 12.6 - Prob. 57SPRCh. 12.6 - Prob. 58SPRCh. 12.6 - Prob. 59SPRCh. 12.6 - Prob. 60SPRCh. 12.6 - Prob. 61SPRCh. 12.6 - Prob. 62SRCh. 12.6 - Prob. 63SRCh. 12.6 - Prob. 64SRCh. 12.6 - Prob. 65SRCh. 12.7 - Prob. 1ACYPCh. 12.7 - Prob. 1BCYPCh. 12.7 - Prob. 1CCYPCh. 12.7 - Prob. 2CYPCh. 12.7 - Prob. 3ACYPCh. 12.7 - Prob. 3BCYPCh. 12.7 - Prob. 1CYUCh. 12.7 - Prob. 2CYUCh. 12.7 - Prob. 3CYUCh. 12.7 - Prob. 4CYUCh. 12.7 - Prob. 5CYUCh. 12.7 - Prob. 6CYUCh. 12.7 - Prob. 7CYUCh. 12.7 - Prob. 8CYUCh. 12.7 - Prob. 9PPSCh. 12.7 - Prob. 10PPSCh. 12.7 - Prob. 11PPSCh. 12.7 - Prob. 12PPSCh. 12.7 - Prob. 13PPSCh. 12.7 - Prob. 14PPSCh. 12.7 - Prob. 15PPSCh. 12.7 - Prob. 16PPSCh. 12.7 - Prob. 17PPSCh. 12.7 - Prob. 18PPSCh. 12.7 - Prob. 19PPSCh. 12.7 - Prob. 20PPSCh. 12.7 - Prob. 21PPSCh. 12.7 - Prob. 22PPSCh. 12.7 - Prob. 23PPSCh. 12.7 - Prob. 24HPCh. 12.7 - Prob. 25HPCh. 12.7 - Prob. 26HPCh. 12.7 - Prob. 27HPCh. 12.7 - Prob. 28HPCh. 12.7 - Prob. 29HPCh. 12.7 - Prob. 30HPCh. 12.7 - Prob. 31STPCh. 12.7 - Prob. 32STPCh. 12.7 - Prob. 33STPCh. 12.7 - Prob. 34STPCh. 12.7 - Prob. 35SPRCh. 12.7 - Prob. 36SPRCh. 12.7 - Prob. 37SPRCh. 12.7 - Prob. 38SPRCh. 12.7 - Prob. 39SPRCh. 12.7 - Prob. 40SPRCh. 12.7 - Prob. 41SPRCh. 12.7 - Prob. 42SPRCh. 12.7 - Prob. 43SRCh. 12.7 - Prob. 44SRCh. 12.7 - Prob. 45SRCh. 12.8 - Prob. 1ACYPCh. 12.8 - Prob. 1BCYPCh. 12.8 - Prob. 2CYPCh. 12.8 - Prob. 3CYPCh. 12.8 - Prob. 1CYUCh. 12.8 - Prob. 2CYUCh. 12.8 - Prob. 3CYUCh. 12.8 - Prob. 4CYUCh. 12.8 - Prob. 5CYUCh. 12.8 - Prob. 6PPSCh. 12.8 - Prob. 7PPSCh. 12.8 - Prob. 8PPSCh. 12.8 - Prob. 9PPSCh. 12.8 - Prob. 10PPSCh. 12.8 - Prob. 11PPSCh. 12.8 - Prob. 12PPSCh. 12.8 - Prob. 13PPSCh. 12.8 - Prob. 14PPSCh. 12.8 - Prob. 15PPSCh. 12.8 - Prob. 16PPSCh. 12.8 - Prob. 17PPSCh. 12.8 - Prob. 18PPSCh. 12.8 - Prob. 19PPSCh. 12.8 - Prob. 20PPSCh. 12.8 - Prob. 21PPSCh. 12.8 - Prob. 22PPSCh. 12.8 - Prob. 23PPSCh. 12.8 - Prob. 24PPSCh. 12.8 - Prob. 25PPSCh. 12.8 - Prob. 26PPSCh. 12.8 - Prob. 27HPCh. 12.8 - Prob. 28HPCh. 12.8 - Prob. 29HPCh. 12.8 - Prob. 30HPCh. 12.8 - Prob. 31HPCh. 12.8 - Prob. 32HPCh. 12.8 - Prob. 33STPCh. 12.8 - Prob. 34STPCh. 12.8 - Prob. 35STPCh. 12.8 - Prob. 36STPCh. 12.8 - Prob. 37SPRCh. 12.8 - Prob. 38SPRCh. 12.8 - Prob. 39SPRCh. 12.8 - Prob. 40SPRCh. 12.8 - Prob. 41SPRCh. 12.8 - Prob. 42SPRCh. 12.8 - Prob. 43SPRCh. 12.8 - Prob. 44SRCh. 12.8 - Prob. 45SRCh. 12.8 - Prob. 46SRCh. 12.8 - Prob. 47SRCh. 12 - Prob. 1GRFCCh. 12 - Prob. 2GRFCCh. 12 - Prob. 3GRFCCh. 12 - Prob. 4GRFCCh. 12 - Prob. 5GRFCCh. 12 - Prob. 6GRFCCh. 12 - Prob. 7GRFCCh. 12 - Prob. 8GRFCCh. 12 - Prob. 9GRFCCh. 12 - Prob. 10GRFCCh. 12 - Prob. 11GRFCCh. 12 - Prob. 12GRFCCh. 12 - Prob. 1MCQCh. 12 - Prob. 2MCQCh. 12 - Prob. 3MCQCh. 12 - Prob. 4MCQCh. 12 - Prob. 5MCQCh. 12 - Prob. 6MCQCh. 12 - Prob. 7MCQCh. 12 - Prob. 8MCQCh. 12 - Prob. 9MCQCh. 12 - Prob. 10MCQCh. 12 - Prob. 11MCQCh. 12 - Prob. 12MCQCh. 12 - Prob. 13MCQCh. 12 - Prob. 14MCQCh. 12 - Prob. 15MCQCh. 12 - Prob. 16MCQCh. 12 - Prob. 17MCQCh. 12 - Prob. 18MCQCh. 12 - Prob. 19MCQCh. 12 - Prob. 20MCQCh. 12 - Prob. 1SGRCh. 12 - Prob. 2SGRCh. 12 - Prob. 3SGRCh. 12 - Prob. 4SGRCh. 12 - Prob. 5SGRCh. 12 - Prob. 6SGRCh. 12 - Prob. 7SGRCh. 12 - Prob. 8SGRCh. 12 - Prob. 9SGRCh. 12 - Prob. 10SGRCh. 12 - Prob. 11SGRCh. 12 - Prob. 12SGRCh. 12 - Prob. 13SGRCh. 12 - Prob. 14SGRCh. 12 - Prob. 15SGRCh. 12 - Prob. 16SGRCh. 12 - Prob. 17SGRCh. 12 - Prob. 18SGRCh. 12 - Prob. 19SGRCh. 12 - Prob. 20SGRCh. 12 - Prob. 21SGRCh. 12 - Prob. 22SGRCh. 12 - Prob. 23SGRCh. 12 - Prob. 24SGRCh. 12 - Prob. 25SGRCh. 12 - Prob. 26SGRCh. 12 - Prob. 27SGRCh. 12 - Prob. 28SGRCh. 12 - Prob. 29SGRCh. 12 - Prob. 30SGRCh. 12 - Prob. 31SGRCh. 12 - Prob. 32SGRCh. 12 - Prob. 33SGRCh. 12 - Prob. 34SGRCh. 12 - Prob. 35SGRCh. 12 - Prob. 36SGRCh. 12 - Prob. 37SGRCh. 12 - Prob. 38SGRCh. 12 - Prob. 39SGRCh. 12 - Prob. 40SGRCh. 12 - Prob. 41SGRCh. 12 - Prob. 42SGRCh. 12 - Prob. 1PTCh. 12 - Prob. 2PTCh. 12 - Prob. 3PTCh. 12 - Prob. 4PTCh. 12 - Prob. 5PTCh. 12 - Prob. 6PTCh. 12 - Prob. 7PTCh. 12 - Prob. 8PTCh. 12 - Prob. 9PTCh. 12 - Prob. 10PTCh. 12 - Prob. 11PTCh. 12 - Prob. 12PTCh. 12 - Prob. 13PTCh. 12 - Prob. 14PTCh. 12 - Prob. 15PTCh. 12 - Prob. 16PTCh. 12 - Prob. 17PTCh. 12 - Prob. 18PTCh. 12 - Prob. 19PTCh. 12 - Prob. 20PTCh. 12 - Prob. 1PSTCh. 12 - Prob. 2PSTCh. 12 - Prob. 3PSTCh. 12 - Prob. 4PSTCh. 12 - Prob. 5PSTCh. 12 - Prob. 6PSTCh. 12 - Prob. 1STPCh. 12 - Prob. 2STPCh. 12 - Prob. 3STPCh. 12 - Prob. 4STPCh. 12 - Prob. 5STPCh. 12 - Prob. 6STPCh. 12 - Prob. 7STPCh. 12 - Prob. 8STPCh. 12 - Prob. 9STPCh. 12 - Prob. 10STPCh. 12 - Prob. 11STPCh. 12 - Prob. 12STPCh. 12 - Prob. 13STP

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