X is point on PQ and Y is a point on PR of a `∆PQR` such that `XY||QR`. If `(PQ)/(XQ)=7/3` and `PR = 6.3 cm` , find YR

In Fig., A, B and C are points on OP, OQ and OR respectively such that AB||PQ and AC||PR .Show that BC||QR .

In figure, PQ is a tangent at a point R of the circle with centre O. If /_TRQ = 30° , find /_PRS .

l is the perpendicular bisector of the line segment PQ and R is a point on the some side of l as P. The line segment QR intersects l at X. Prove that PX + XR = QR .

In Fig.6.56,PS is the bisector of angleQPR of trianglePQR .Prove that (QS)/(SR)=(PQ)/(PR) .

O is a point within the ∆ABC . P, Q , R are three points on OA , OB and OC respectively such that PQ||AB and QR||BC . Prove that RP||CA .

S and T are points on sides PR and QR of triangle PQR such that angleP=angleRTS .Show that triangleRPQ~triangleRTS

In figure 12 PS is a diameter of a circle whose radius is 6cm . Two pint Q and R are taken on PS such that PQ= QR = RS . Two Semi-circles are drawn with PQ and QS as their respective diameters as shown in the figure. find the perimeter and the area of the shaded region shown in figure. (Take pi=3.14 )

∆PQR is right angled at Q and the points S and T trisect the side QR. Prove that 8PT^2 = 3PR^2 + 5PS^2 .

In Fig 12,PS is a diameter of a circle whose radius is 6 cm.Two points Q and R are taken on PS such that PQ=QR=RS.Two semicircles are drawn with PQ and QS as their respective diameters as shown in the figure.Find the perimeter and the area of the shaded region shown in figure. (pi=3.14)

let A(1,3) and B(2,7) be two points. point P divides the line segment joining the point A(-1,3) and B(9,8) such that 'AP/BP=k/1'. if P lies on the line x- y + 2=0 find the value of k.