In an acute angled triangle `A B C ,r+r_1=r_2+r_3a n d/_B >pi/3,` then `b+2c<2a<2b+2c` `b+4c<4a<2b+4c` `b+4c<4a<4b+4c` `b+3c<3a<3b+3c`

In an acute angled triangle ABC, r + r_(1) = r_(2) + r_(3) and angleB gt (pi)/(3) , then

With usual notations in a triangle A B C , if r_1=2r_2=2r_3 then 4a=3b (b) 3a=2b 4b=3a (d) 2a=3b

In A B C , if r\ : r_1: R=2\ : 12\ :5, where all symbols have their usual meaning, then A B C is an acute angled triangle A B C is an obtuse angled triangle A B C is right angled which is not isosceles A B C is isosceles which is not right angled

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle ABC(R being the radius of the circumcircle)? a,sin A,sin B(b)a,b,c,a,sin B,R(d)a,sin A,R

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 ' 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)

In a DeltaABC , if r=r_2+r_3-r_1 and Agt pi/3 then range of s/a contains (A) (1/2, 2) (B) [1,2) (C) (1/2, 3) (D) (3,oo)

In a triangle ABC Let BC=a, CA=b, AB=c and r_(1), r_(2) & r_(3) be the radii of ex-circles opposite to vertices A B&C respectively. If r_(1)=2r_(2)=2r_(3) then 3(a/b)=