Let `A B C` be a triangle with incentre at `Idot` Also, let `Pa n dQ` be the feet of perpendiculars from `AtoB Ia n dC I ,` respectively. Then which of the following results are correct? `(A P)/(B I)=(sinB/2cosC/2)/(sinA/2)` (b) `(A Q)/(C I)=(sinC/2cosB/2)/(sinA/2)` `(A P)/(B I)=(sinC/2cosB/2)/(sinA/2)` (d) `(A P)/(B I)+(a Q)/(C I)=sqrt(3)if/_A=60^0`

Let A and B be square matrices of the same order such that A^(2)=I and B^(2)=I , then which of the following is CORRECT ?

In A B C ,(sinA(a-bcosC)/(sinC(c-bcosA)= -2 (b) -1 (c) 0 (d) 1

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_3)/((r-r_1)(r-r_2)(r-r_3))

Let A B C be a triangle such that /_A C B=pi/6 and let a , ba n dc denote the lengths of the side opposite to A , B ,a n dC respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,a n dc=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) 2+sqrt(3) (d) 4sqrt(3)

Let I be the incentre of A B C having inradius rdotA I ,B Ia n dC I intersect incircle at D , Ea n dF respectively. Prove that area of D E F is (r^2)/2(cosA/2+cosB/2+cosC/2)

Show that (1+sinA)/(cosA)+(cosB)/(1-sinB)=(2sinA-2sinB)/(sin(A-B)+cosA-cosB)

ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

In any triangle ABC prove that (a^(2)sin(B-C))/(sinA)+(b^(2)sin(C-A))/(sinB)+(c^(2)sin(A-B))/(sinC)=0

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

(sin2A+sin2B+sin2C)/(sinA+sinB+sinC)i se q u a lto 8sin(A/2)sin(B/2)sin(C/2) (b) 8cos(A/2)cos(B/2)cos(C/2) 8tan(A/2)tan(B/2)tan(C/2) (d) 8cot(A/2B)/2cot(C/2)