. Elements of geometry : containing books I to III. BGO, Thm must chord BC = cAord /J . Take the centres B . Then, if • ABCbe applied to • DOT, so that A coincides with /., /; with E, and an- /,v,v falls on arc EHF, :? arc BGC arc /:///•, .. 0 will coincide wil Then v B coincidea with I. ;,uA c with /•. ,\ chord BC must coincide with and be equal tu chord EF. ,. K. D. Ex. 1. The two straight lines in a circle, which join the• wo parallel chorda, are i qua! t one another. ! . [| • qual chords of a circle, cut one anotl i the circle, thai Book III. 1 NOTE 4. IW Note 4. On the Syrmnetr
. Elements of geometry : containing books I to III. BGO, Thm must chord BC = cAord /J . Take the centres B . Then, if • ABCbe applied to • DOT, so that A coincides with /., /; with E, and an- /,v,v falls on arc EHF, :? arc BGC arc /:///•, .. 0 will coincide wil Then v B coincidea with I. ;,uA c with /•. ,\ chord BC must coincide with and be equal tu chord EF. ,. K. D. Ex. 1. The two straight lines in a circle, which join the• wo parallel chorda, are i qua! t one another. ! . [| • qual chords of a circle, cut one anotl i the circle, thai Book III. 1 NOTE 4. IW Note 4. On the Syrmnetrical j *ro\ erties of the Circle withregard to its diameter. The brief remarks on Symmetry in pp. 107, 108 may nowhe extended in the Gojlowing way : A figure is said to be symmetrical with regard to a line,when every perpendicular to the line meets the figure atpoints which aie equidistant from the line. Hence a Circle is Symmetrical with regard to its Diameter,because the diameter bisects every chord, to which it is Further, suppose AB to be a diameter of the circleiCBI), of which 0 is the centre, and CD to be a chordperpendicular to AB. Then, if lines be drawn as in the diagram, we know thatAh bisects (1.) The chord CD, III. I. (2.) The arcs CAD and CBD, III. 26. (3.) The angles CAD, COD, CBD, and the reflexangle I I. 4. Also, chord CB=chord I>B, I. 4. and chord AC= chord A D I. 4. These Symmetrical relations should be carefully observed,because they are often suggestive of methods for the solutionof probiems. .6c [Book lit Proposition XXX. bisect a given arc
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