3 geometry question.(Please list the step)?

9:
Since they are tangents, BF=BD=x, CE=CF=y, AD=AE=z
Also, we can use pythagoras theroem to find AB=30
Since CF is perpendicular to CE, y is equal to the radius
We can create 3 simultaneous equations:
1) AC=AE+EC=y+z=24
2) BC=BF+FC=x+y=18
3) AB=AD+DB=z+x=30
If we add all 3 of these together: y+z+x+y+z+x=24+18+30
So 2x+2y+2z=72
So x+y+z=36
We want to find y, so 36=x+z+y=30+y, so y=6
So the answer is D: 6

10:
Since P is the midpoint of AT, and O is the midpoint of AB:
OP is perpendicular to AB
OP=radius=2
BT=2OP=4
So the area of triangle AOP is 1/2*2*2=2
The area of segment BOP is 1/4*π*r^2=1/4*π*2^2=1/4*π*4=π
The area of triangle ABT is 1/2*4*4=8
So the shaded area is given by 8-2-π=6-π
So the answer is C: 6-π

12:
Draw a line from each of a and c to a point on the opposite side of the circle to b, and label the angle they meet at d
Opposite angles of a cyclic quad add up to 180, so b+d=180
Angle at the centre of a circle = twice the angle at the circumference, so 2d=aOc, so d=1/2 aOc
So b+1/2 aOc=180, so 360-2b=aOc
Since internal angles of a quadrilateral sum to 360, a+b+c+aOc=360, a+b+c+360-2b=360, a+c-b=0, so a+c=b
So the answer is A: b

9.
In the figure AB, AC and BC are three tangents touching the circle at D, E and F respectively.
If AC = 24, BC =18 and ∠ACB = 90°.
Find the radius of the circle.
Answer Choice:
D. 6

10.
In the figure, TB touches the semi-circle at B.
TA cuts the semi-circle at P such that TP = PA.
If the radius of the semi-circle is 2,
find the area of the shaded region.
Answer choice:

12.
In the figure, O is the centre of the circle.
Find a + c.
Answer choice:
E. 360 - 2b

I found one:
For (9) answer is D (6) reference: http://www.efunda.com/math/areas/circleinscribetrianglegen.cfm