If the equations of the sides of a triangle are ` a_(r)x+b_(r)y = 1 , r = 1 ,2,3 ` and the orthocentre is the origin then prove that
`a_1a_2 +b_1b_2= a_2a_3+ b_2b_3 =a_3a_1+b_3b_1`

If the lines a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 cut the coordinae axes at concyclic points, then prove that a_1a_2=b_1b_2

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

If the sides be a,b,c, than find (r_(1)- r)(r _(2)+r_(3)).

If the area of the triangle formed by the points (2a,b), (a+b, 2b+a) and (2b, 2a) be Delta_(1) and the area of the triangle whose vertices are (a+b, a-b), (3b-a, b+3a) and (3a-b, 3b-a) be Delta_(2) , then the value of Delta_(2)//Delta_(1) is

In a triangle ABC, if r_1 + r_3 + r = r_2 , then find the value of (sec^2 A + cos^2 B-cot^2 C) ,

A triangle A B C with vertices A(-1,0),B(-2,3/4), and C(-3,-7/6) has its orthocentre at Hdot Then, the orthocentre of triangle B C H will be

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

If in a triangle (1-(r_1)/(r_2))(1-(r_1)/(r_3))=2 then the triangle is right angled (b) isosceles equilateral (d) none of these

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))