In the figure \$m ∥ l\$, \$n ∥ p\$ and n and p are transversals. If AC \$= 2x + y\$ and BD \$= 3 - x\$, AD \$= x - 4y\$ and CB \$= 4 - 2x + 2y\$, find the valus of x and y.

A) \$x = 3\$ and \$y = 4\$

B) \$x = 1\$ and \$y = 6\$

C) \$x = 6\$ and \$y = 3\$

D) \$x = 1\$ and \$y = 1\$

If H is the mid-point of AD and BE, BH = 130 and HE = 15k, find the value of k.

A) 9

B) 4

C) 3

D) 5

In a circle with centre A, AE = AD = AC = AB, AE \$= x\$ , CA \$= 5 - y\$, DE \$= x + 4\$ and DC \$= 2y\$. Find the values of a and y.

A) \$x = 2\$ and \$y = 3\$

B) \$x = 4\$ and \$y = 4\$

C) \$x = 4\$ and \$y = 5\$

D) \$x = 2\$ and \$y = 4\$

Two circles with center E and G are orthogonal, F is the mid point of HG, HG bisects \$\angleH\$ and \$\angleG\$, and AB is perpendicular to HG. If AH \$= 4x\$, AG \$= 7 - 3y\$, HB \$= x + 1\$ and BG \$= 2y\$, find the values of x and y

A) \$x = 2\$ and \$y = 3\$

B) \$x = 4\$ and \$y = 4\$

C) \$x = 1\$ and \$y = 1\$

D) \$x = 2\$ and \$y = 4\$

AB is the diameter of the circle with center C, DA and BC are the tamgents of the circle, AC \$= x + 1\$, BC = y, CD \$= 3x + 3y\$ and CE \$= 9 + 2y\$, find the values of x and y.

A) \$x = 3\$ and \$y = 6\$

B) \$x = 5\$ and \$y = 4\$

C) \$x = 2\$ and \$y = 3\$

D) \$x = 4\$ and \$y = 6\$