In Fig.
, sides AB and AC of `DeltaABC` are extended to points P and Q respectively. Also `anglePBC < angleQCB`. Show that `AC > AB`.

In the given Fig , Sides AB and AC of a DeltaABC are produced to E and D respectively. If respective bisectors BO and CO of angleCBE and angleBCD intersect each other at point O, prove that angleBOC = 90^@-1/2 angleBAC .

In the given Fig , Sides AB and AC of a DeltaABC are produced to E and D respectively. If respective bisectors BO and CO of angleCBE and angleBCD intersect each other at point O, prove that angleBOC = 90^@-1/2 angleBAC .

if a line intersects sides AB and AC of a DeltaABC at D and E respectively and is parallel to BC, prove that (AD)/(AB)=(AE)/(AC) (see Fig. 6,13).

In Fig. , AB > AC , show that AB > AD .

In Fig. , AB > AC , show that AB > AD .

Dand E are the mid-points of the sides AB and AC of DeltaABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is

In Fig, 6.21 , A, B and C are points on OP, OQ and OR respectively such that AB||PQ and AC||PR. Show that BC||QR.

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

In Fig. , ABCD is a trapezium in which AB || DC and P, Q are mid-points of AD and BC respectively. If CP and BA when produced meet at E, prove that PQ=1/2(AB+DC) .