. Elements of geometry : containing books I to III. And the figure is said to be inscribed in the circle. Book III] FFOFOSI7VOX I. 23 Proposition I. Theorem. The line, which bisects a chord of a circle at right angles,must contain the Let ABC he the given ©.Let the st. line CE bisect the chord AB at rt. angles in D. Then the centre of the G must lie in CE. For if not, let 0, a pt. out of CE, be the centre ;and join OA, OD, OB. Then, in as ODA, ODB,V AD = BD, and DO is common, and OA = OB; .: l ODA = / ODB; I. c. and .-. l ODB is a right i. I. Def. 9 But L CDB is a right i , by constructi
. Elements of geometry : containing books I to III. And the figure is said to be inscribed in the circle. Book III] FFOFOSI7VOX I. 23 Proposition I. Theorem. The line, which bisects a chord of a circle at right angles,must contain the Let ABC he the given ©.Let the st. line CE bisect the chord AB at rt. angles in D. Then the centre of the G must lie in CE. For if not, let 0, a pt. out of CE, be the centre ;and join OA, OD, OB. Then, in as ODA, ODB,V AD = BD, and DO is common, and OA = OB; .: l ODA = / ODB; I. c. and .-. l ODB is a right i. I. Def. 9 But L CDB is a right i , by construction ;.*. L ODB = z CM>, which is impossible ;.. 0 is not the it may be shewn that no point, out of CE, c;m be thecentre, and .\ the centre must lie in CE. Cor. // the chord CE be bisected in F} then F is centreOf the circle, 124 UCL fDS ELEMENTS. [Book III. Proposition II. Theorem. Jf any two joints In taken in (he circumference of a n,< straight line, which joins them, must fall within thecircle.
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