`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.

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.

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concylic.

Let A B C be an isosceles triangle in which A B=A Cdot If D ,\ E ,\ F be the mid-points of the sides B C ,\ C A\ a n d\ A B respectively, show that the segemtn A D\ a n d\ E F bisect each other at right angles.

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B E*C F=A B^2dot Prove that the line E F always passes through a fixed point.

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

In an isosceles triangle A B C with A B=A C , a circle passing through B and C intersects the sides A Ba n dA C at Da n dE respectively. Prove that DE∣∣BC Bdot

G is the centroid of triangle A B Ca n dA_1a n dB_1 are rthe midpoints of sides A Ba n dA C , respectively. If "Delta"_1 is the area of quadrilateral G A_1A B_1a n d"Delta" is the area of triangle A B C , then "Delta"//"Delta"_1 is equal to a.3/2 b. 3 c. 1/3 d. none of these