...— cos — 2 2 Analogous expressions of course obtain for n and rc in terms of R. 1. Expression for the distance between the centres of the inscribed and circumscribed circles of a triangle in terms of the radii of these two circles. Let 0 be the centre of the inscribed, aud (/ of the circumscribed...

...generators of the coiifocal hyperboloid of one sheet through the vertex. 2795. (Proposed by S. TEBAY, BA) — Find the average square of the distance between...and circumscribed circles of a triangle inscribed iu a given circle. I. Solution by the Eev. J. WOLSTENHOLME/MA If a be the radius of the given circle,...

...plane P, and let one of the foci of the section be at P ; this being so, reciprocating origin at F, the section of the reciprocal surface by the plane...inscribed in a given circle. I. Solution by the Rev. J. WOLSTEKHOLME, MA If a be the radius of the given circle, x radius of an inscribed circle, square of...

...centre of the circumscribed circle, then, cos. A -f cos. B + cos. C = \/£. Solution by EJ If. — The square of the distance between the centres of the inscribed and circumscribed circles of a triangle ia R' — 2Rr. • Thus if the inscribed circle pass through the centre of the circumscribed circle...

...middle points of IEZ, IEt ; therefore it is the nine-point circle of the triangle PROP. X. To find the distance between the centres of the inscribed and circumscribed circles of a triangle. Let ABC be a triangle, O the centre, and R the radius of the circumscribing circle. From 0 draw OD...

...the circles which have been noticed in Arts. 248. ..252; as an example we will find an expression for the distance between the centres of the inscribed and circumscribed circles of a triangle. Let ABG be a triangle; let 0 be the centre of the circumscribed circle. From 0 draw a perpendicular...

.... S (m . Hence, from (4), (m . Equation (4) can be employed to prove the well-known expression for the distance between the centres of the inscribed and circumscribed circles of a plane triangle, viz. : under which form Lagrange expresses the distance of the centre of gravity of...

...(see Mecaniqw Analytlque, p. 61). Equation (4) can be employed to prove the well-known expression for the distance between the centres of the inscribed and circumscribed circles of a plane triangle, viz. D being the distance between the centres, and r and R being their radii, respectively....

...(see Mecanique Analytique, p. 61). Equation (4) can be employed to prove the well-known expression for the distance between the centres of the inscribed and circumscribed circles of a plane triangle, viz. : D2 = JB2-272r, D being the distance between the centres, and r and R being their...

...(z'+yi-aI-b2+rs)44{bV+ay-a'62-f1(a' + b')} _ 0, from 9' = 4Д9' and the values in (4949). 4972 Ex. (ii.) — The distance between the centres of the inscribed and circumscribed circles of a triangle is thus found, by employing the values of в, в', and Д in (4947), to be D = v/^i 2rr'), as in (936)....