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

ABC is an isosceles triangle with AB=AC and D is a point on an BC such that ADbotBC to prove that angleBAD=angleCAD ,

In a triangle ABC, D is the mid point of side AC such that BD=1/2AC . Show that angleABC is a right angle.

In Fig. D is a point on side BC of triangleABC such that (BD)/(CD) = (AB)/(AC) . Prove that AD is the bisector of angleBAC .

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 is a point on side BC of triangleABC such that (BD)/(DC)=(AB)/(AC) . Prove that, AD is bisector of angleBAC . .

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see Fig. 7.29). Show that AD = AE.

Prove m:n theorem in a Delta ABC , a point D is taken on side BC such that BD:DC is m:n. Then prove that(1) (m+n)cottheta= mcotalpha -ncotbeta (2) (m+n)cottheta= ncotB-mcotC

ABCD is a parallelogram. P is any point on AD, such that AP = 1/3AD and Q is a point on BC such that CQ = 1/3BC . Prove that AQCP is a parallelogram.

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then ar (BDE)= 1/4 ar(ABC).

In Delta ABC , P is mid point of BC, then BD= BC (True/false)