...expression for the angular radius of the small circle inscribed in a given spherical triangle. If D be the distance between the centres of the inscribed and circumscribed circles of a given spherical triangle, r, R their respective radii, prove that sin2 D = sin2 (R — 2•) - cos*...

...A2 whence, F=rS:R, and hence, F : M= — 2 Rr ; Such, then, is the relation connecting the radii and distance between the centres of the inscribed and circumscribed circles of a A. Now, holding the circles fixed, let us see how we can vary the A. Taking the one centre as origin,...

...centres of the three escribed circles are equal to 4Rsin^-A, •••, and to asec-JA, •••. 8. The square of the distance between the centres of the inscribed and circumscribed circles is ir — 2Rr. 9. Prove the equations : r = (s — a) tan i A, r =8 tau i л tan AB tan ¿с, г =...

...radii of the circles touching AC and AB respectively, S = S '~ s — 6' s~ s — с 105. То find the Distance between the Centres of the Inscribed and Circumscribed Circles* of a Triangle. Let I and O be the incentre and circumcentre, respectively, of the triangle ABC, IA and 1C bisect the...

...the stations, the distance between the stations, and the angular diameter of the sun. 9. Prove that the distance between the centres of the inscribed and circumscribed circles of a triangle is v/7i2-2.Rr, where r, R are radii of these circles. If the sum of the pairs of radii of the escribed...

...W, whence M'X3 = M'O . M'R. We have, however, that M'X = MQ = OM, hence OM* = M'O . M'R (1). OM is the distance between the centres of the inscribed and circumscribed circles of triangle ABC, and OM = d3 = i* — 2 rp, where r and p are the radii respectively of the circumscribed...

...centres of the three escribed circles are equal to 4K sin £A . . ., and to a sec £A . . .. 8. The square of the distance between the centres of the inscribed and circumscribed circles is R2Prove the equations : 9. 'r = (s — a) tan£A. 10. r = s tan £A tan £B tan £c. Prove the equations...

...circle to the centres of the three escribed circles are equal to 4Rsin£A . . ., and to asec£-A 8. The square of the distance between the centres of the inscribed and circumscribed circles is R* — 2Rr. Prove the equations : 9. -r = (s — a) tan£A. Prove the equations : 12. n = abc/4:K....

...inscribed circle of a triangle. Prove that r (cot - + cot — + cot - ) = £(a + 6 + c). 12. Prove that 8 the distance between the centres of the inscribed and circumscribed circles of a triangle is given by the equation 82 = R2-2Rr. Q Show that if R = 2r for the triangle ABC, then 2 (cos A) =...