`A D` is a median of ` A B C` . The bisector of `/_A D B` and `/_A D C` meet `A Ba n dA C` in `Ea n dF` respectively. Prove that `E F B Cdot`

In quadrilateral ABCD,AO and BO are the bisectors of /_A and /_B respectively.Prove that /_AOB=(1)/(2)(/_C+/_D)

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 a parallelogram A B C D ,\ the bisector of /_A also bisects B C at Xdot Find A B : A D

Let A D be a median of the A B Cdot If A Ea n dA F are medians of the triangle A B Da n dA D C , respectively, and A D=m_1,A E=m_2,A F=m_3, then(a^2)/8 is equal to (a)m_2^2+m_3^2-2m_1^2 (b) m_1^2+m_2^2-2m_3^2 (c)m_1^2+m_3^2-2m_2^2 (d) none of these

In Figure, A B C D is a parallelogram and /_D A B=60^0dot If the bisectors A P\ a n d\ B P of angles A\ a n d\ B respectively, meet at P on C D , prove that P is the mid-point of C D

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

In a A B C , If L a n d M are points on A B a n d A C respectively such that L M B Cdot Prove that: a r ( A B M)=a r ( A C L)

In a parallelogram A B C D , A B=10 c m , A D=6c mdot The bisector of /_A meets D C in E , A E a n d B C produced meet at Fdot Find the length C Fdot