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 a1a2 +b1b2= a2a3+ b2b3 =a3a1+b3b1

The combined equation of three sides of a triangle is (x^2-y^2)(2x+3y-6)=0 . If (-2,a) is an interior point and (b ,1) is an exterior point of the triangle, then 2

The exradii of a triangle r_(1),r_(2),r_(3) are in HP , then the sides a,b,c are

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

ln a triangle with sides a, b, c if r1 gt r2 gt r3 (which are the ex-radii), then

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

The mid points of the sides of a triangle A B C along with any of the vertices as the fourth point make a parallelogram of area equal to: a r\ ( A B C) (b) 1/2a r\ ( A B C) 1/3a r\ ( A B C) (d) 1/4\ a r\ ( A B C)

In a triangle , if r_(1) = 2r_(2) = 3r_(3) , then a/b + b/c + c/a is equal to

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

A triangle has two of its sides along the lines y=m_1x&y=m_2x where m_1, m_2 are the roots of the equation 3x^2+10 x+1=0 and H(6,2) be the orthocentre of the triangle. If the equation of the third side of the triangle is a x+b y+1=0 , then a=3 (b) b=1 (c) a=4 (d) b=-2

A triangle has two of its sides along the lines y=m_1x&y=m_2x where m_1, m_2 are the roots of the equation 3x^2+10 x+1=0 and H(6,2) be the orthocentre of the triangle. If the equation of the third side of the triangle is a x+b y+1=0 , then a=3 (b) b=1 (c) a=4 (d) b=-2