`O` is the circumcenter of ` A B Ca n dR_1, R_2, R_3` are respectively, the radii of the circumcircles of the triangle `O B C ,O C A` and OAB. Prove that `a/(R_1)+b/(R_2)+c/(R_3),(a b c)/(R_3)`

If I is the incenter of A B Ca n dR_1, R_2,a n dR_3 re, respectively, the radii of the circumcircles of the triangles I B C ,I C Aa n dI A B , then prove that R_1R_2R_3=2r R^2dot

If I is the incenter of Delta ABC and R_(1), R_(2), and R_(3) are, respectively, the radii of the circumcircle of the triangle IBC, ICA, and IAB, then prove that R_(1) R_(2) R_(3) = 2r R^(2)

If ' O ' is the circum centre of the A B C and R_1,\ R_2,\ R_3 are the radii of the circumcircle of triangle O B C ,\ O C A\ a n d\ O A B respectively then a/(R_1)+b/(R_2)+c/(R_3) has the value equal to (a b c)/(2R^3) (b) (R^3)/(a b c) (c) (4)/(R^2) (d) (a b c)/(R^3)

O is the circumcentre of the triangle ABC and R_(1),R_(2),R_(3) are the radii of the circumcirclesof the triangles OBC,OCA and OAB respectively,then (a)/(R_(1))+(b)/(R_(2))+(c)/(R_(3)), is equal to

Prove that : (r_1-r)/(a) +(r_2-r)/(b) = (c )/(r_3) .

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

In a right angled DeltaABC, angleA=90^(@) . If AC = b, BC = a, AB = c and r and R are respectively radii of incircle and circumcircle of the triangle then prove that 2(r + R) = b + c

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)