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

in the adjoining figure, Delta PQR is an equilateral triangle. Point S is on seg QR such that QS = 1/3 QR , Prove that 9 PS^(2) = 7 PQ^(2)

The perpendicular PS on the base QR of Delta PQR intersects QR at S, such that QS=3 SR. Prove that 2PQ^(2)=2PR^(2)+QR^(2) .

Two circles with centres O and O' of radii 3cm and 4 cm, respectively intersect at two points P and Q, such that OP and O' P are tangents to the two circles. Find the length of the common chord PQ.

The straight lines 3x + 4y - 5 = 0 and 4x -3y = 15 intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1, 2) are

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 the adjoining figure, M is the midpoint of QR. anglePRQ = 90^(@) prove that PQ^(2) = 4 PM^(2) - 3 PR^(2)

In Delta PQR , given that S is a point on PQ such that ST || QR and (PS)/(SQ) = 3/5 . If PR = 5.6 cm , then find PT .

In the adjoining figure, point Q is the point of contact of tangent and circle . If PQ = 12, PR = 8, then find Ps and RS .

In triangle Delta PQR , E and F are points on the sides PQ and PR respectively. State whether EF ||QR or not? (iii) PQ = 1.28 cm PR = 2.56 cm PE = 0.18 cm and PF = 0.36 cm