Find the Radius of escribed circle `(i) r_1 = Delta/(s-a) = s tan (A/2) = 4 R sin (A/2) Cos (B/2 )Cos (C/2)`

Derive the Formula of inradius (i) Delta/ s (ii) ( s-a) tan A/2 (iii) 4R sin A/2sin B/2sin C/2

4R cos ((A) / (2)) cos ((B) / (2)) cos ((C) / (2)) =

If I_(1), I_(2), I_(3) are the centers of escribed circles of Delta ABC , show that the area of Delta I_(1) I_(2) I_(3) is (abc)/(2r)

cos2B + cos2A-cos2C = 1-4sin A sin B cos C

Show that, 4 R r cos ""A/2cos ""B/2 cos ""C/2 =Delta

If inside a big circle exactly n(nlt=3) small circles, each of radius r , can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then the radius of big circle is r(1+cos e cpi/n) (b) ((1+tanpi/n)/(cospi/pi)) r[1+cos e c(2pi)/n] (d) (r[s inpi/(2n)+cos(2pi)/n]^2)/(sinpi/n)

cos A + cos B + cos C = 1 + 4sin ((A) / (2)) sin ((B) / (2)) sin ((C) / (2))

DEF is the triangle formed by joining the points of contact of the incircle with the sides of the triangle ABC : prove that its sides are 2r cos (A)/(2), 2r cos (B)/(2)," and " 2r cos (C )/(2) .