Area of the shaded

A circle of diameter of 30cm, enclose in a square of 30cm x 30cm, the square is divided in 3 parts 10cm x 30cm, the lower part is divided into a right angle triangle of 30cm (base) and 10cm (height), find the area between the 'circle' and the right angle triangle.

Answers
The drawing does not show what I want.
timothy
11 November 2013
My drawing did not post correctly either.  Where in the drawing is the right angle of the triangle?
tutor777
11 November 2013
Hi Timothy,All you have to do is draw a diagram as you have said, so: 30cm diameter circle -> draw around it the 30cm x 30cm square -> draw two lines across the square making the three 10cm divisions -> along the bottom division draw a diagonal line (thus making the 30cm base from the square and the 10cm height from the division) which will give you a right-angled triangle.Then look at the shape for the area you want, if you describe this area a bi better I can help you further, until now, draw the diagram! :)
Rulank K.
11 November 2013
Try to draw using whiteboard but the result come out different. I will think of another way.
timothy
12 November 2013
Find the area mark "X"
timothy
12 November 2013
math-problem.pdf
timothy
12 November 2013
Hi TimothyI'm guessing this is an A-level question... There doesn't appear to be an easy trick to get the answer, so it will take a few steps. First find the intersection points of the diagonal line and the circle (call them A and B, you can do this by writing equations for the line and the lower half of the circle and solving). Then you can find the angle between those two intersection points and the center of the circle (O), and the rest should be straight forward (area of right angle triangle minus (area of sector minus area of triangle AOB)). Hope this helps, give me a shout if you need to go through the required techniques in more detail.Andy
mettudh
23 November 2013
I totally agree with Rulank, draw the diagram out properly, then the solution often presents itself :)
Hen S.
29 November 2013
Let first write equation of circle and equation of diagonal in Cartesian coordinate syste. Find the intersection points of the diagonal  and the circle.Let us call them A and B. Calculate length of chord AB by using distance formula. Apply cosine rule to calculate central angle AOB,where O is  center of the circle.Required area is equal to area of the  right angle triangle minus area of the minor segment AB. 
pramodpandey
16 December 2013
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