...diameter is called a semicircumfe.re.nee., and each portion of the circle is called a semicircle. 13. THEOREM. — In the same circle or in equal circles, if two arcs are equal, their chords will be equal, and con~ versefy, if two chords are equal their arcs will be equal.' This...

...diameter is called a semidrcumference, and each portion of the circle is called a semicircle. 13. — In the same circle or in equal circles, if two arcs are equal, their chords will be equal, and conversely if two chords are equal their arcs will be equal — . This...

...two tangents intercept equal arcs of the same circumference they will be parallel. THEOREM vII. In the same circle, or in equal circles, if two arcs are equal, they will have equal chords, which will le equally distant from the centre. If the arcs are unequal and...

...two tangents intercept equal arcs of the same circumference they will be parallel. THEOREM VII. In the same circle, or in equal circles, if two arcs are equal, they will have equal chords, which will oe equally distant from the centre. Jf the arcs are unequal and...

...the student state and prove other converses to Propositions III. IV and VI.] PROPOSITION VII. 151. Theorem.— In the same circle, or in equal circles, if two arcs are equal, the chords which subtend them are equal; and, conversely, if two chords are equal, the subtended arcs...

...state and prove other converses to Propositions III, IV and VI.] PROPOSITION VII. 151. Theorem.—In the same circle, or in equal circles, if two arcs are equal, the chords which subtend them are equal; and, conversely, if two chords are equal, the subtended arcs...

...degrees is also used for arcs. Similarly for minutes, seconds, and other measurements. Theorem 2. In the same circle or in equal circles, if two arcs are equal, the central angles which they subtend are equal also, and of two unequal arcs the greater subtends...

...degrees is also used for arcs. Similarly for minutes, seconds, and other measurements. Theorem 2. In the same circle or in equal circles, if two arcs are equal, the central angles which they subtend are equal also, and of two unequal arcs the greater subtends...

...circumference two equal chords, PA, PB, are drawn. Prove (1) that these chords subtend equal centraI angles, (2) that they subtend equal arcs. 252. The...Theorem. In the same circle or in equal circles, if two arcf are equal they are subtended by equal chords, and of two unequal minor arcs the greater is subtended...

...text-books and examination papers, that the student needs to become familiar with it. PROPOSITION II. 181. Theorem. In the same circle or in equal circles, if two arcs are equal, the central angles which they subtend are equal also, and of two unequal arcs the greater- subtends...