In adjacent figure, sides AB and AC of `DeltaABC` are extended to points P and Q respectively. Also, `/_PBC < /_QCB`. Show that AC > AB.

In the given figure sides AB and AC of triangleABC , are extended to point P and Q respectively. Also anglePBC lt angleQCB . Show that AC gt AB .

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 .

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

In the figure, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q , and R respectively. Prove that (i) AB+CQ=AC+BQ (ii) Area (DeltaABC)=1/2 ("Perimeter of" DeltaABC)xx r

In the adjoining figure, D and E are the mid-points of AB and AC respectively. If DE = 4 cm , then BC is equal to :

In the adjacent figure AB || CD. Find the values of x, y and z.

In the given figure, AB||DC and AD||BC show that DeltaABC ~= Delta CDA .

GD and GH are respectively the bisectors of angleACB and angleEGF such that D and H lie on sides AB and FE of DeltaABC and and DeltaEFG respectively. If DeltaABC~DeltaFEG , show that: (CD)/(GH) =(AC)/(FG)

In the given figure, a circle is inscribed in a DeltaABC such that it touches the sides AB, BC, and CA at points D, E, and F respectively. If the lengths of the sides AB, BC, and CA are 12 cm, 8 cm, and 10 cm respectively, find the lengths of AD, BE, and CF.