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 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) (c) 2RsinAsinBsinC (d) delta/R

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 ,sinA ,sinB (b) a , b , c , a ,sinB ,R (d) a ,sinA ,R

In an acute angle triange ABC, a semicircle with radius r_(a) is constructed with its base on BC and tangent to the other two sides r_(b) and r_(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))

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

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

If R_1 is the circumradius of the pedal triangle of a given triangle A B C ,a n dR_2 is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_3,R_4 then the value of sum_(i=1)^ooR_i , where R (circumradius) of A B C is 5 is 8 (b) 10 (c) 12 (d) 15

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

If H is the orthocentre of triangle A B C ,R= circumradius and P=A H+B H+C H , then P=2(R+r) (b) maxof P is 3R minofP is 3R (d) P=2(R-r)

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to 1 (b) 9 (c) 27 (d) none of these

In Delta ABC if r_1=2r_2=3r_3 and D is the mid point of BC then cos/_ADC=