In a triangle ABC, the vertices A,B,C are at distances of p,q,r fom the orthocentre respectively. Show that ` aqr+brp+cpq=abc`

In any triangle ABC ,the distance of the orthocentre from the vertices A, B,C are in the ratio

In a triangle ABC , the sides a , b , c are in G.P., then the maximum value of angleB is

Vertices of a variable acute angled triangle ABC lies on a fixed circle. Also a, b, c and A, B, C are lengths of sides and angles of triangle ABC, respectively. If x_(1),x_(2) and x_(3) are distances of orthocentre from A, B and C, respectively, then the maximum value of ((dx_(1))/(da)+(dx_(2))/(db)+(dx_(3))/(dc)) is

In triangle ABC, the measure of angleB is 90^(@) , BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sin F ?

The sum of the first p , q , r terms of an A.P. are a , b , c respectively. Show that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

The sum of the first p , q , r terms of an A.P. are a , b , c respectively. Show that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

The sum of the first p , q , r terms of an A.P. are a , b , c respectively. Show that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

If the angle A,B,C of a Delta ABC are in A.P then :-

If pth,qth and rth terms of an A.P. are a, b, c respectively, then show that (i) a(q-r)+b(r-p)+c(p-q)=0

A triangle ABC with vertices A(-1,0),B(-2,3/4) & C(-3,-7/6) has its orthocentre H, then the orthocentre of triangle BCH will be