Elementary plane geometry : inductive and deductive / by Alfred Baker . etimes givenas the definition of a tangent. 3. Since a diameter bisects every chord to which itis at right angles, therefore a line drawn through thebisection of a chord and at right angles to it, mustbe a diameter. Hence if the centre of any circle benot indicated, we may reach it by the following con-struction : Draw any chord AB. Bisectit at C. Draw DCE perpendicu-lar to AB. DE must passthrough the centre. Hence, bi-secting DE at F, F must bethe centre of the circle. We may describe circles with-out marking their centre
Elementary plane geometry : inductive and deductive / by Alfred Baker . etimes givenas the definition of a tangent. 3. Since a diameter bisects every chord to which itis at right angles, therefore a line drawn through thebisection of a chord and at right angles to it, mustbe a diameter. Hence if the centre of any circle benot indicated, we may reach it by the following con-struction : Draw any chord AB. Bisectit at C. Draw DCE perpendicu-lar to AB. DE must passthrough the centre. Hence, bi-secting DE at F, F must bethe centre of the circle. We may describe circles with-out marking their centres byplacing a piece of thin woodor cardboard under the station-ary point of the compasses, removing this piece of woodor cardboard when the circle is described. Circles being thus described, or being obtained bymarking with the pencil about a round object placedon the paper (coin, bottom of ink bottle, plate, &c.),attempts should be made to locate the centre by theeyes judgment. We may afterwards test the correct-ness of this by making the preceding construction,. 74 Geometry.
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