Prnciples of Plane Geometry

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Prnciples of Plane Geometry
J W James Wallace Macdonald
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When do circles touch each other internally? When externally ?
30 PLANE GEOMETRY.
157. When is an angle inscribed in a circle? in. (/\ 158. When is an angle inscribed in a segment ? m.
159. When is a polygon inscribed in a circle ? m.
a. What is the relation of the circle to the polygon } 160. When is a circle inscribed in a polygon ? in.
a. What is the relation of the polygon to the circle ?
161. What are concentric circles? Illustration.
162. When will circles be equal?
163. What is an angle
...at the centre ?
Proposition I. A Theorem.
164. The diameter of a circle is an axis of symmetry.
Corollary. The diameter bisects the circle and its cir- cumference.
Proposition li. A Theorem.
165. A straight line cannot intersect the circumference of a circle at more than two points.
See Book I. , Proposition XVI. , Corollary.
Proposition III. A Theorem.
166. The diameter is longer than any other chord.
BOOK III. 31 Proposition IV. A Theorem.
167. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and conversely, if the chords are equal, the arcs also are equal.


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