Let `O(0,0),P(3,4),` and `Q(6,0)` be the vertices of triangle `O P Q` . The point `R` inside the triangle `O P Q` is such that the triangles `O P R ,P Q R ,O Q R` are of equal area. The coordinates of `R` are

P(1, 4), Q(3, -9) and R(-5, 2) are the vertices of a triangle. Find the length of the median passing through Q.

If the point (0,0),(2,2sqrt(3)), and (p,q) are the vertices of an equilateral triangle, then (p ,q) is

Let p,q,r be the sides opposite to the angles P,Q, R respectively in a triangle PQR if r^(2)sin P sin Q= pq , then the triangle is

Let O(0,0),A(2,0),a n dB(1, 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(P, O B),d(P,A B)] , where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

Let 0-=(0,0),A-=(0,4),B-=(6,0)dot Let P be a moving point such that the area of triangle P O A is two times the area of triangle P O B . The locus of P will be a straight line whose equation can be

The vertices of a triangle are (p q ,1/(p q)),(q r ,1/(q r)), and (r p ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are

Let p,q,r be the altitudes of a triangle with area s and perimeter 2t. Then the value of 1/p+1/q+1/r is

Two points P(a,0) and Q(-a,0) are given. R is a variable point on one side of the line P Q such that /_R P Q-/_R Q P is a positive constant 2alphadot Find the locus of the point Rdot

The base vertices of an isosceles triangle PQR are Q (1,3) and R(-2, 7). The vertex P can be-