In a `triangle OAB`,E is the mid point of OB and D is the point on AB such that `AD:DB=2:1` If OD and AE intersect at P then determine the ratio of `OP: PD` using vector methods

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = CM . X is a point on the side OB such that OX = 2XB. The line XC is produced to meet OA in Y. Then (OY)/(YA)=

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

In a triangle ABC, D is a point on BC such that AD is the internal bisector of angle A . Let angle B = 2 angle C and CD = AB. Then angle A is

ABC is a right triangle , right angled at A and D is the mid point of AB . Prove that BC^(2) =CD^2 +3BD^(2) .

In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley, such that B D=2D Ca n dA E=3E Cdot Let P be the point of intersection of A Da n dB Edot Find B P//P E using the vector method.

In Delta ABC if r_1=2r_2=3r_3 and D is the mid point of BC then cos/_ADC=

In a triangle P Q R ,Sa n dT are points on Q Ra n dP R , respectively, such that Q S=3S Ra n dP T=4T Rdot Let M be the point of intersection of P Sa n dQ Tdot Determine the ratio Q M : M T using the vector method .

Let O A C B be a parallelogram with O at the origin and O C a diagonal. Let D be the midpoint of O Adot using vector methods prove that B Da n dC O intersect in the same ratio. Determine this ratio.

Let O A C B be a parallelogram with O at the origin and O C a diagonal. Let D be the midpoint of O Adot using vector methods prove that B Da n dC O intersect in the same ratio. Determine this ratio.