`/_PBC`, `/_QBC`, `/_RBC` are three isosceles triangles on the same base BC. Show that P, Q, R are collinear.

/_\PBC and /_\ QBC are two isosceles triangles on the same side of the some base. Show that the PQ is the right bisector of BC.

If Fig.6.44 ABC and DBC are two triangles on the same base BC.If AD intersects BC atb O,show that (ar(ABC))/(ar(DBC))=(AO)/(DO)

triangleBAC and triangleBDC are two right-triangle on the same side of the base BC.If AC ans DB intersect each other at a point P,show that APxxPC=DPxxPB .

If pth, qth and rth term of an A.P. are in A.P., show that p, q, r also are in A.P.

Prove that the points P,Q,R are collinear. P(1,4),Q(3,-2),R(-3,16)

Prove that the points P,Q,R are collinear. P(1,5) ,Q(3,14), R(-1,-4)

Two triangles ABC and DBC are in the same side of the common base BC. Lines drawn parallel to BA and BD from any point E on BC intersect AC and DC at the points P and Q respectively. Show that PQ is parallel to AD.

Prove that the points P,Q,R are collinear. P(a, b+c), Q(b, c+a), R(c, a+b)

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 .

Show that the triangle formed by the three points (5,-2),(6,4) and (7,-2) is isosceles.