Plane and solid geometry . nequal,the central angle that intercepts tlxe greater arc is thegreater. (Hint. Lay off the smaller central angle upon the greater.) 295. Def. A fourth part of a circumference is called ^quadrant. From Prop. II it is evidentthat a right angle at the centerintercepts a quadrant on the cir-cumference. ThuSj two _L diam-eters AB and CD divide thecircumference into four quadrants,AC, CB, BD, and DA. 296. Def. A degree of arc, or anarc degree, is the arc interceptedby a central angle of one degree. 297. A right angle contains ninety angle degrees (§ 71);therefore, since e
Plane and solid geometry . nequal,the central angle that intercepts tlxe greater arc is thegreater. (Hint. Lay off the smaller central angle upon the greater.) 295. Def. A fourth part of a circumference is called ^quadrant. From Prop. II it is evidentthat a right angle at the centerintercepts a quadrant on the cir-cumference. ThuSj two _L diam-eters AB and CD divide thecircumference into four quadrants,AC, CB, BD, and DA. 296. Def. A degree of arc, or anarc degree, is the arc interceptedby a central angle of one degree. 297. A right angle contains ninety angle degrees (§ 71);therefore, since equal central angles intercept equal arcs on thecircumference, a quadrant contains ninety arc degrees. Again, four right angles contain 360 angle degrees, and fourright angles at the center of a circle intercept a complete cir-cumference ; therefore, a circumference contains 360 arc , a semicircumference contains 180 arc degrees. Ex. 408. Divide a given circumference into eight equal arcs ; sixteen equal 118 PLANE GEO:\IETRY Ex. 409. Divide a given circumference into six equal arcs; threeequal arcs ; twelve equal arcs. Ex. 410. A diameter and a secant perpendicular to it divide a cir-cumference into two pairs of equal arcs. Ex. 411. Construct a circle which shall pass through two given pointsA and B and shall have its center in a given line c. Ex. 412. If a diameter and another chord are drawn from a point ina circumference, the arc intercepted by the angle between them will bebisected by a diameter drawn parallel to the chord. Ex. 413. If a diameter and another chord are drawn from a point ina circumference, the diameter which bisects their intercepted arc will beparallel to the chord. Proposition III. Theorem 2d8. In equal circles, or in the same circle, if twochords are equal, they subtend equal arcs; conversely,if two arcs are equal, the chords that subtend tliem areequal.
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