practice problems pending

Q0.
In a ||gram ABCD, does the diagonal AC bisect the angle DAB?

Q1.



M,N,D are midpoints of AB,AC,BC.
X,Y are midpoints of NC,ND.
Find [MNXY]/[ABC].

S1.
Let [ABC] = f => [AMN] = f/4
=> [BCNM] = 3f/4

[CND] = f/4 => [NYX] = f/16
[MNXY] = [NYX] + [MNY] => we need to find [MNY] now.

[BDNM] = [BCNM] - [NDC] = f/2
[BDM] = [NDM] = f/4
[MNY] = [DMY] = f/8

=> [MNXY] = [NYX] + [MNY] = f/16 + f/8 = 3f/16

Q2. ABCD is a parallelogram. X divides AB in the ratio 3:2.
Y divides CD in the ratio 4:1.
XY intersects AC at Z. Find (AZ : AC).


S2.







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