By Samuel Smith Keller

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Touches circle, V. from it D hence AD > A to AD > AC, but AB; hence AB FE. '. AB is is AC = AB. shorter than any other line perpendicular to FE. Plane Geometry. 53 Fig. 46. 94. its extremity, 95. A Cor. I. is straight line perpendicular to a radius at tangent to the Cor. II. circle. A perpendicular to a tangent at the point of contact, passes through the centre of the circle. Proposition VIII. 96. Construction. To draw a circumference through any same straight line. three points not in the Statement: Let A, B and C three points not in the line; to same be any straight pass a circumference through them.

Other side, is one half the vertical angle of the triangle. THE CIRCLE. Definitions. 74. curved A circle is a plane figure whose boundary line, every point of point within, called its which is equally distant is a from a center. The boundary curve is called the circumference. 75. The radius is a straight line joining the center to any point on the circumference. The word radius often refers to the length of this line, not necessarily to the line itself. Plane Geometry. 46 76. The diameter is a straight line through the centre on the circumference.

And > OMR, SM = Z OMR and prove the converse equals OM and MR (by hypothesis), SR > OR SR > AB - OR. EXERCISE. State MOR of Prop. III. ) Plane Geometry. 50 Proposition IV. 90. and A diameter perpendicular the arc at C and Analysis: that is, a chord bisects the chord A be any circle and BD a chord in it, FE (or the radius AE) J_ to BD bisects Statement: Let then the diameter BD to subtends. it also the arc The BED is C the middle point of BD, evidently dependent upon the equality proof that BC = CD, at E.