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`

Given P=(1,0) and Q=(-1,0) and R is a variable point on one side of the line PQ such that /_RPQ - /_RQP = pi /4 . The locus of the point R is

S and T are points on sides PR and QR of DeltaP Q R such that /_P=/_R T S . Show that DeltaR P Q ~DeltaR T S .

In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P >2P S

Given that P(3,1),Q(6. 5), and R(x , y) are three points such that the angle P R Q is a right angle and the area of R Q P is 7, find the number of such points Rdot

If P ,Q and R are three collinear points such that vec P Q= vec a and vec Q R = vec bdot Find the vector vec P R .

In Figure, T is a point on side Q R of P Q R and S is a point such that R T=S Tdot Prove That : P Q+P R > Q S

/_P Q R =100^(@) , where P, Q and R are points on a circle with centre O. Find /_O P R

Show that the relation R on the set A of points in a plane, given by R={(P ,\ Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further show that the set of all points related to a point P!=(0,\ 0) is the circle passing through P with origin as centre.

Show that the relation R on the set A of points in a plane, given by R={(P ,\ Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further show that the set of all points related to a point P!=(0,\ 0) is the circle passing through P with origin as centre.

PQR is a triangle right-angled at P and M is a point on QR such that P M_|_Q R . Show that P M^2=Q M.M R .