In fig., D is a point on side BC of `triangleABC` such that `(BD)/(DC)=(AB)/(AC)` . Prove that, AD is bisector of `angleBAC` .
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D is any point on side AC of triangleABC with AB=AC show that CD>BD.

In the fig. AB=AC , D is the point in the interior of triangleABC such that angleDBC=angleDCB . Prove that AD bisects angleBAC and triangleABC

D is a point on side BC of Delta ABC such that AD = AC (see Fig. 7.47). Show that AB > AD.

In fig. D and E are points on side BC of triangleABC such that BD=CE and AD=AE. Show that triangleABDequivtriangleACE

In an equilateral triangle ABC. D is a point on side BC such that BD=1/3 BC. Prove that 9AD^2=7AB^2 .

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

Let ABC be a right triangle with length of side AB=3 and hyotenus AC=5. If D is a point on BC such that (BD)/(DC)=(AB)/(AC), then AD is equal to

In the fig. X and Y are respectively two points on equal sides AB and AC of triangleABC such that AX=AY. Prove that CX=BY

In the fig. side BC of triangleABC is produced to from ray BD and CE||BA Prove that angleACD=angleA+angleB

Triangle ABC and DBC are on the same base BC with A,D on opposite sides of line BC, such that ar(triangleABC) = ar(triangleDBC) . Prove that BC bisects AD.