In a triangle A B C ,Da n dE are points ...

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.

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In a A B C ,D and E are points on sides A B a n d A C respectively such that B D=C E . If /_B=/_C , show that DE || BC .

In Figure, A B=C D . Prove that B E=D E\ a n d\ A E=C E , where E is the point of intersecting of A D\ a n d\ B C .

In Figure, A D=A E\ a n d\ D\ a n d\ E are points on B C such that B D=E Cdot Prove that A B=A C

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

In Figure, A B C is a triangle in which A B=A Cdot Point D and E are points on the sides AB and AC respectively such that A D=A Edot Show that the points B , C , E and D are concyclic.

A B C is an isosceles triangle in which A B=A Cdot If Da n dE are the mid-points of A Ba n dA C respectively, prove that the points B ,C ,Da n dE are concylic.

In triangle A B C ,points D , Ea n dF are taken on the sides B C ,C Aa n dA B , respectively, such that (B D)/(D C)=(C E)/(E A)=(A F)/(F B)=ndot Prove that triangle D E F=(n^2-n+1)/((n+1)^2) triangle(A B C)dot

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .

A B C is a triangle with /_B greater than /_C ,Da n dE are points on B C such that A D is perpendicular to B Ca n dA E is the bisector of angle Adot Complete the relation /_D A E=1/2()+/_C]dot

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