- N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in areal co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.

00=ordi- The escribed circle opposite the angle A is - sqr +(s - c)rp Hates.

00In this article the equations to the more important circles - the circumscribed, inscribed, escribed, self-conjugate--will be given; reference should be made to the article Triangle for the consideration of other circles (nine-point, Brocard, Lemoine, &c.); while in the article Geometry: Analytical, the principles of the different systems are discussed.

00The equation to the circumcircle assumes the simple form a fry +bra+ca(3= o, thecentre being cos A, cos B, cos C. The inscribed circle is cos zA -V a +cos 1B -J (3 +cos 2C ¦ y = o, with centre Trill ea a= (3 = y; while the escribed circle opposite the angle A is cos 2A' - a+sin 2B A / 0+sin IC y=o, with centre Hates.

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