The exradii `r_1,r_2` and `r_3` of ` /_\A B C` are in H.P. Show that its sides `a , ba n dc` are in `AdotPdot`

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P.show that its sides are in A.P .

In A B C , right-angled at C , if tanA=sqrt((sqrt5-1)/2) , show that the sides a , ba n dc are in G.P.

The radii r_1, r_2,r_3 of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m^2a n d its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b : c be sqrt(3):sqrt(2) . Find angle Adot

a ,b ,c x in R^+ such that a ,b ,a n dc are in A.P. and b ,ca n dd are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_3=p vec r_1+q vec r_2, then show that p+q=1.

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))

Let P Q R be a triangle of area with a=2,b=7/2,a n dc=5/2, w h e r ea , b ,a n dc are the lengths of the sides of the triangle opposite to the angles at P ,Q ,a n dR respectively. Then (2sinP-sin2P)/(2sinP+sin2P)e q u a l s