One and ONLY ONE problem/question per post.

In the figure below, ADC is a chord of a circle centre O and passing
through the points A, B and C. BD is a perpendicular bisector 
of the chord AC.  AD=8 cm and BD=2 cm. Calculate the area of the 
minor segment ABCD.

I'll just do the first one for you.

Here are the steps to find the area of a segment of a circle.

1. Identify the radius of the circle and label it 'r'.
2. Identify the central angle AOC made by the arc of the segment and label it 
.
3. Find the area of triangle AOC using the formula  or .
4. Find the area of the sector OABC using the formula
, if θ is in degrees (or)
, if θ is in radians.
5. Subtract the area of the triangle OAC from the area of the sector OABC to
find the area of the segment ABCD.

So we need to find radius r and angle θ.



Draw in OD (in green).  Since OA, OB, OC are all radii, with length r,
and since BD=2 cm, OD = OB-BD = r-2 



To find radius r, we use the Pythagorean theorem on right triangle OAD:



To find θ, we use:





Now we go back to the given figure:



For step 3, we find the area of triangle OAC either by




or .

For step 4, we find the area of the entire sector ABCO either by 

, if θ is in degrees

^""/360^o)*pi*r^2}}}
(or)
, if θ is in radians.



Notice there's a slight difference between those two values.

Finally we do step 6 and subtract the area of the triangle from the area of the
sector



(or)



Edwin