P and Q re tow interior points on te side BC of `/_\ABC `such that , `BP ||BQ` and `BC.PQ=BP. CQ` and AQ bisects `/_PAC` using vector method prove that AQ and AB are mutually perpendicular

P and Q are the points on sides AB and AC respectively of a DeltaABC , such that PQ||BC .If AP|PB=2:3 and AQ=4 cm , then the length of AC is ….. Cm .

Three points P, Q, R lie on the side BC of triangle ABC such that BP = PQ = QR = RC. If G be centroid of DeltaABC then what is ratio of areas of DeltaPGR and DeltaABC .

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

P and Q are points on the sides AB and AC of a ABC such that BP = CQ = x cm, PA = 6cm, AQ = 20cm, BC = 25cm. If PAQ and quadrilateral BPQC have equal areas, then the value of x is (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm

Let ABC be a triangle with circumcenre O. The points P and Q are interior points of the sides Let K, L and M be the mid points of the segments BP, CQ and PQ respectively, and let tau be the circle passing through K, L and M. Suppose that the line PQ is tangent to the circle tau. Prove that OP=OQ.

If P and Q are points on the sides AB and AC respeactively of triangleABC , if PQ||BC,l AP= 2 cm , AB = 6 cm and AC= 9 cm find AQ.

A circle is touching the side BC of ABC at P and touching AB and AC produced at Q and R respectively.Prove that AQ=(1)/(2)(Perimeter of ABC)

In a triangleABC P and Q are points on AB and AC respectively and PQ||BC. Prove that the median AD bisects PQ.

Let ABC and PQR be any two triangles in the same plane. Assume that the perpendiculars from the points A, B, C to the sides QR, RP, PQ respectively are concurrent. Using vector methods or otherwise,prove that the perpendiculars from P, Q, R to BC, CA, AB respectively are also concurrent.