In Fig , the side QR and `DeltaPQR` is produced to a point S. If the bisector of `lfloorPQR and lfloorPRS` meet at point T the prove that `lfloor QTR=(1)/(2) lfloorQPR.`

In Fig , sides QP and RQ and RQ of DeltaPQR are produced to points S and T respectively . If lfloorSRP = 135^(@) and lfloorPQT=110^(@) , " find " lfloorPRO .

In the adjacent figure the sides AB and AC of Delta ABC are produced to points E and D respectively. If bisectors BO and CO of angleCBE and angleBCD respectively meet at point O, then prove that angleBOC = 90^(@)-(1)/(2) angleBAC .

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

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed . Show that ar (ABCD) = ar (PBQR)

If S is a point on side PQ of a Delta PQR such that PS = QS = RS , then find PR^(2) + QR^(2)

In Fig .D is a point on side BC of DeltaABC such that (BD)/(CD) =(AB)/(AC) prove that AD is the bisector of angleBAC.

Find the equation of the right bisector of the line segment joining the points (3, 4) " and " (-1, 2) .

In the triangle PQR, is a point on PR such that QN_|_PR . If PN. NR = QN^(2) , prove that lfloorPQR=90^(@) .

In the given figure sides QP and RQ of ΔPQR are produced to points S and T respectively. If angleSPR = 135^(@) and anglePQT = 110^(@) , find anglePRQ.

In Fig. two chords AB and CD of a circle intersect each other at the point P ( when produced ) outside the circle prove that DeltaPAC~DeltaPDB