In `DeltaPQR,Pq=PR` and S is the mid-point of PQ. A line drawn from S parallel to QR, intersects the line PR at T. Prove that PS = PT.

If S is the mid-point of side QR of a DeltaPQR , then prove that PQ+PR=2PS .

If Q is a point on the side SR of a triangle Delta PSR such that PQ = PR then prove that PS > PQ

Consider the circle x^2+y^2 -8x-18y +93=0 with the center C and a point P(2,5) out side it. From P a pair of tangents PQ and PR are drawn to the circle with S as mid point of QR. The line joining P to C intersects the given circle at A and B. Which of the following hold (s)

The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.

In the adjoining figure, DeltaPQR is formed by the sides PQ, QR and RP which are drawn parallel to sides AB,BC and CA respectively of DeltaABC. Prove that " "PQ+QR+RP=2(AB+BC+CA).

Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

In trapezium ABCD, AB || DC and L is the mid-point of BC. Through L, a line PQ || AD has been drawn which meets AB in P and DC produced in Q. Prove that ar (ABCD) = ar (APQD).

In Delta PQR ,PQ =PR . A is a point in PQ and B is a point in PR , so that QR = RA = AB = BP Find the vlaue of angle Q.

M and N are mid point on sides QR and PQ respectively of /_\ PQR , right-anggled at Q. Prove that : 4PM^(2)= 4PQ^(2)+QR^(2) .

M and N are mid- point on sides QR and PQ respectively of /_\ PQR , right-anggled at Q. Prove that : PM^(2)+RN^(2)= 5 MN^(2) .