Elements of geometry and trigonometry . required (Prop. IX.). If the point A lies without the circle,join A and the centre, by the straightline CA : bisect CA in O ; from O as acentre, with the radius OC, describe acircumference intersecting the given cir-cumference in B ; draw AB : this will bethe tangent required. For, drawing CB, the angle CBA be-ing inscribed in a semicircle is a rightangle (Prop. XVIII. Cor. 2.) ; thereforeAB is a perpendicular at the extremityof the radius CB ; therefore it is a tan-gent. Scholium, When the point A lies without the circle, therewill evidently be always t
Elements of geometry and trigonometry . required (Prop. IX.). If the point A lies without the circle,join A and the centre, by the straightline CA : bisect CA in O ; from O as acentre, with the radius OC, describe acircumference intersecting the given cir-cumference in B ; draw AB : this will bethe tangent required. For, drawing CB, the angle CBA be-ing inscribed in a semicircle is a rightangle (Prop. XVIII. Cor. 2.) ; thereforeAB is a perpendicular at the extremityof the radius CB ; therefore it is a tan-gent. Scholium, When the point A lies without the circle, therewill evidently be always two equal tangents AB, AD, passingthrough the point A : they are equal, because tlie right angledtriangles CBA, CDA, have the hypothenuse CA common, andthe side CB = CD; hence they are equal (Book I. Prop. XVII.);hence AD is equal to AB, and also the angle CAD to as there can be but one hne bisecting the angle BAC^ itfollows, that the Une which bisects the angle formed by twotangents^ must pass through the centre of the PROBLEM XV. To inscribe a circle in a. given tîiangle. Let ABC be the given triangle. Bisect the angles A and B, bythe lines AO and BO, meeting inthe point O ; from the point O,let fall the perpendiculars OD,OE, OF, on the three sides of thetriangle: these perpendiculars willall be equal. For, by construe-
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
