If lines `p x+q y+r=0,q x+r y+p=0a n dr x+p y+q=0` are concurrent, then prove that `p+q+r=0(w h e r ep ,q ,r` are distinct`)dot`

If lines px+qy+r=0,qx+ry+p=0 and rx+py+q=0 are concurrent,then prove that p+q+r=0 (where p,q,r are distinct )

If p,q and r are in AP,then prove that (p+2q-r)(2q+r-p)(r+p-q)=4pqr

Prove that px^(q-r)+qx^(r-p)+rx^(p-q)>p+q+r, where p,q,r are distinct and x!=1

In Fig. 6.15, /_P Q R=/_P R Q , then prove that /_P Q S=/_P R T .

If p, q, r are in G.P. and the equations, p x^2+2q x+r=0 and dx^2+2e x+f=0 have a common root, then show that d/p ,e/q ,f/r are in A.P.

If px + qy + r = 0 and qx + py + r = 0 (x != y) , then show that the value of x + y " is " (-r)/(p) or (-r)/(q)

If p and q are the roots of the equation x^2 - 15x + r = 0 and. p - q = 1 , then what is the value of r?