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

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot

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

In acute angled triangle A B C ,A D is the altitude. Circle drawn with A D as its diameter cuts A Ba n dA Ca tPa n dQ , respectively. Length of P Q is equal to /(2R) (b) (a b c)/(4R^2) 2RsinAsinBsinC (d) Δ /R

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then b : c is equal to

If A,B,C are the angles of an acute angled triangle and cos(B+C-A)=0, sin (C+A-B)=(sqrt(3))/2 , find the values of A,B , and C.

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

If H is the orthocentre of triangle ABC, R = circumradius and P = AH + BH + CH , then (a) P = 2 (R + r) (b) max. of P is 3R (c) min. of P is 3R (d) P = 2 (R -r)

Consider an acute angled Delta ABC. Let AD, BE and CF be the altitudes drawn from the vertice to the opposite sides. Prove that : (EF)/(a)+ (FD)/(b)+ (DE)/(c)= (R+r)/(R ).

A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are the circumradius, inradius, and altitude, respectively, then (R+r)/h is equal to (a) 4 (b) 2 (c) 1 (d) 3

In a triangle ABC, r^2+r_1^2+r_2^2+r_3^2+a^2+b^2+c^2 is equal to (where r is inradius and r_1,r_2,r_3 are exradil a,b,c are the sides of DeltaABC )