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10 Oct 2004, 01:15
Kudos
Bookmarks
This is one of Akamai's .. nice one...
https://www.manhattangmat.com
Praetorian
https://www.manhattangmat.com
Praetorian
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10 Oct 2004, 06:07
Kudos
Bookmarks
7/5.
Draw a radius from B to BZ (to from diameter YZ).
r = 360/pi (from the length-of-an-arc formula).
Draw a radius from B to A, results in a 'small' semicircle with diameter of 360/pi. Area of this 'small' circle is 90(180)/pi. You have to add it to the area of the sector YBC in the denominator of the ratio, and subtract it from the area of the semicircle in the numerator (together with the area of sector ABZ).
Now, angle YXA = 105, draw a line from X to Z, forming angle YXZ inscribed in a semicircle, = 90 degrees. Then angle AXZ is 105-90=15, and results in arc AZ of 30, with angle ABZ = 30 degrees.
From there, get the area of sector ABZ = 30/360pir^2 = (3*360)/pi
For the ratio, in the numerator, you have Area of semicircle - area of ABZ - area of 'small' semicircle
in the denominator, you have area of ABZ + area of small 'semicircle'
solve it out, and you should get 180*210/180*150 = 210/150=7/5.
After this one, I guess I will retire for today!
[/b]
Draw a radius from B to BZ (to from diameter YZ).
r = 360/pi (from the length-of-an-arc formula).
Draw a radius from B to A, results in a 'small' semicircle with diameter of 360/pi. Area of this 'small' circle is 90(180)/pi. You have to add it to the area of the sector YBC in the denominator of the ratio, and subtract it from the area of the semicircle in the numerator (together with the area of sector ABZ).
Now, angle YXA = 105, draw a line from X to Z, forming angle YXZ inscribed in a semicircle, = 90 degrees. Then angle AXZ is 105-90=15, and results in arc AZ of 30, with angle ABZ = 30 degrees.
From there, get the area of sector ABZ = 30/360pir^2 = (3*360)/pi
For the ratio, in the numerator, you have Area of semicircle - area of ABZ - area of 'small' semicircle
in the denominator, you have area of ABZ + area of small 'semicircle'
solve it out, and you should get 180*210/180*150 = 210/150=7/5.
After this one, I guess I will retire for today!
[/b]
