Elementary plane geometry : inductive and deductive / by Alfred Baker . 80 4^ Geometry. angles, therefore the triangles CDB, CEB are equal inall respects. But the triangle CAF is equal in allrespects to CDB; and the triangle CAG is equal in allrespects to the triangle CEB. Therefore the trianglesCAF and CAG are equal in all respects. Hence AF, AGare equal, and the angles at A are equal. In practice, an easy way todraw a tangent from anypoint A, outside the circle,is as follows: Place the set-square so that one of itssides passes through A andthe other through C, the cen-tre of the circle. Then
Elementary plane geometry : inductive and deductive / by Alfred Baker . 80 4^ Geometry. angles, therefore the triangles CDB, CEB are equal inall respects. But the triangle CAF is equal in allrespects to CDB; and the triangle CAG is equal in allrespects to the triangle CEB. Therefore the trianglesCAF and CAG are equal in all respects. Hence AF, AGare equal, and the angles at A are equal. In practice, an easy way todraw a tangent from anypoint A, outside the circle,is as follows: Place the set-square so that one of itssides passes through A andthe other through C, the cen-tre of the circle. Then soadjust the instrument thatthe right angle rests on the circumference at, say, , a tangent through A, may then be drawn. Construct a circle of radius IJ in., and draw anyline through its centre. From points on this line atdistances from the centre 2, 2^, 3 in., draw tangents tothe 3. Let a circle be describedwith centre A, and the tan-gent at any point C be drawn;and let, with centre B, onAC, and radius BC, anothercircle be drawn. Then bothcircles have CD for touching the same lineat the same point, they aresaid to touch one another,—in this case internally.
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