...be in Harmonical Progression, when a, b, c are in Arithmetical Progression. 13. Find the radius of the circle which touches one side of a triangle and the other two produced. VII.—ALGEBRA, TRIGONOMETRY, AND ANALYTICAL GEOMETRY. 1. Investigate the expansion of a"...

...Hence Similarly Hence the required equation is cos — V<* + cos — V/3 + cos — /v/7 = 0. л л л 315. To. find the equation to the circle which touches...0 and the other sides produced, a is positive and ß and 7 are negative. Hence by Art. 309, the form of the equation to the circle must be V(- fa) +...

...points, is — , where r is the radius of the inscribed circle. 24. Three circles are described, each of which touches one side of a triangle and the other two sides produced. If D be the point of contact of the side £C, E that of AC, and F that of AB, shew that AE=BD, BF=CE,...

...the triangle. For example Js(sa)(sV)(tc) _ /(t-'j)(tV)(tc) >--- - - : 103 135. To find the radius of the circle which touches one side of a triangle and the other two sides produced. Let ABC be a triangle ; and let 0, be the centre of th circle which touches BC and the other sides produced....

...example r _ ab sin C _ db sin C! 2* ~ a + b + <; ' 135. To find tlie radius of the circle which towhes one side of a triangle and the other two sides produced. Let ABC\& a triangle; and let 0, be the centre of the circle which touches SC and the other sides produced....

...meet will be the centre of the required circle. The demonstration will be similar to that in IV. 4. A circle which touches one side of a triangle and the other two sides produced, is called an escribed circle of the triangle. We can also describe a triangle equiangular to a given...

...meet will be the centre of the required circle. The demonstration will be similar to that in IV. 4. A circle which touches one side of a triangle and the other two sidus produced, is called an escribed circle of the triangle. We can also describe a triangle equiangular...

...- a = Л-F, ) = s - 6 = .BF, CD = s - c = CE. 119. To ^nef the radius of the escribed circle, ie of the circle which touches one side of a triangle, and the other two produced. Let FDE be such a circle touching BC, iea'i&D and the other sides produced in E, F. O its...

...,C s'-- : cos*- : cos - , and the required equation is Ti „- -3A Ti C1 — INSCRIBED CIECLE. 351. To find the equation to the circle which touches one side of the triangle of reference and the two others produced. Let the circle touch BC, and AB, AC produced;...

...cos'Therefore the required equation is A , B ,0 G , A cos -=• ya + cos — vp + cos -¿- V7 = 0. 325. To find the equation to the circle which touches one...0 and the other sides produced, a is positive and ß and 7 are negative. Hence by Art. 318, the form of the equation to the circle must be V(- la) +...