If a point Q lies between two points P and R such that PQ = QR, prove that PQ = `1/2`PR.

If a point Q lies between P and R such that PQ = QR , prove that PR = 2 PQ .

If P, Q, R are 3 points on a line and Q lies between P and R, then prove that PQ=PR+RQ

If two circles touching both the axes intersect at two points P and Q where P=(3,1) then PQ=

PQR is an isosceles triangle whose equal sides PQ and PR are at right angles S and T are points on PQ such that QS = 6 (SP) " and " QT = 2 (TP) " and if" angle PRS = theta , angle PRT = phi then

If A =(1,2,3) and B=(3,5,7) and P, Q are the points on AB such that AP= PQ =QB,then the mid point of PQ is

If a line through A(1, 0) meets the lines of the pair 2x^2 - xy = 0 at P and Q. If the point R is on the segment PQ such that AP, AR, AQ are in H.P then find the locus of the point R.

The point 'E' divides the segment PQ internally in the ratio 1 : 2 and R is any point not on the line PQ. If F is a point on QR such that QF : FR = 2 : 1 then show that EF is parallel to PR.