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Four+circles.jpg

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Four+circles.jpg

(Note: above that should be a hyperlink to the diagram...)

In the figure attached below the large circle has radius 1 and center O.  PQ and RS are its diameters and are perpendicular. OP, OR, OQ, and OS are diameters of the four small circles below. The point T is a point of intersection of two of the small circles, as shown. Let a1 be the area of the shaded region between the arcs TS, TQ, and QS (see the picture above). Furthermore, let a2 be the area of the shaded region between the two arcs OT. What is the value of a1-a2?

Need answer and explination as soon as possible!!! Thank you so much!!!!!!!!

Jul 15, 2017

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Here is the actual hyperlink, but without the variables but, I considering it is a circle you can plug the pairs of variables and variables in the correct areas

http://www.davidmaroto.info/Four-Circles

if not... the image is calles Four+Circles.jpg but it has labels and two shaded reagions which are key...

if you know how I could possible insert shapes please let me know how to I can put to diagram on here the correct way...

Jul 15, 2017
#2
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Area of the big circle is pi*2^2 = 4pi

Area of the little cirlce is  pi*1^2 = pi

Now

$$\text{area of big = 4 area of little} - 4A_2+4A_1\\ 4\pi=4pi- 4A_2+4A_1\\ so\\ - 4A_2+4A_1=0\\ A_2=A_1\\ A_1-A_2=0$$

I can explain better if you need me to :)

OR if anyone who is watching wants me too. :)

Jul 15, 2017
edited by Melody  Jul 15, 2017