If \$AF ∥ BC\$, D is the mid-point of BC, AD is perpendicular to EF and BC, \$\angle EAB = \angle FAC\$, AB \$= 2x + 3\$, AC \$= 3y + 1\$, BD \$= x\$ and DC \$= y + 1\$, find the values of x and y.

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

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

C) \$x = 1\$ and \$y = 0\$

D) \$x = 5\$ and \$y = 3\$

AB = BC = CD = DE = EB = EF = FA, BE is perpendicular to AC and FD, find the values of a and b.

A) \$a = 15^\circ\$ and \$b = 25^\circ\$

B) \$a = 25^\circ\$ and \$b = 35^\circ\$

C) \$a = 30^\circ\$ and \$b = 45^\circ\$

D) \$a = 45^\circ\$ and \$b = 30^\circ\$

ABCD is a square, AC and DB are diagonals of square, AE = 2x - 6 and CE = -3y + 10, BE = 5x and ED = 4y - 6, Find the values of x and y.

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

B) \$x = 2\$ and \$y = 2\$

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

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

ACBD is a cyclic quadrilateral, AB is the diagonal of the quadrilateral also the longest chord for the circle. Also AB is angluar bisector of \$\angle CAD\$ and \$\angle CBD\$. If AD = 3x, DB = 10- 7y, CB = x and AC = 2y + 7, find the length of DB.

A) \$BD = 6\$

B) \$BD = 3\$

C) \$BD = 5\$

D) \$BD = 2\$

Triangle ACD is incribed in a circle with centre O, AB bisects \$\angle A\$, AB = BC = BD, AC = x - 1, AD = y, CB = x and BD = 5 - y.

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

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

C) \$x = 5\$ and \$y = 3\$

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