Formulae OF inradius(r)||ex-radius(r1,r2,r3)

Problem Base on Inradius (r) and Ex-Radius (R1,R2,R3)||The Ambiguous Case OF Δ

Prove that r_(1)^(2)+r_(2)^(2) +r_(3)^(3) +r^(2) =16R^(2) -a^(2) -b^(2) -c^(2). where r= in radius, R = circumradius,, r_(1), r_(2), r_(3) are ex-radii.

In an equilateral triangle, inradius r , circumradius R and ex-radius r_1 are in A.P. (b) G.P. (c) H.P. (d) none of these

In a /_\ABC (with usual notations) if ex-radii r_(1) , r_(2) , r_(3) are in H.P then (a+c)/b is

In an equilateral triangle the inradius and the circum-radius is connected by (1)r=4R(2)r=(R)/(2)(3)r=(R)/(3)(4)r=(r)/(sqrt(3))

How many such triangles can exist where s=5,r=1 and R=3 (where s= semi perimeter, r = inradius; R= circum radius)

Find the ratio of circum radius (R) to inradius (r) of a triangle whose sides are 4,6 and 8.

Three circles with radius r_(1), r_(2), r_(3) touch one another externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 2 . The value of ((r_(1)r_(2)r_(3))/(r_(1)+r_(2)+r_(3))) is equal to