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 ^{a}1_{ }be the area of the shaded region between the arcs TS, TQ, and QS (see the picture above). Furthermore, let ^{a}2 be the area of the shaded region between the two arcs OT. What is the value of ^{a}1-^{a}2?

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

Trinityvamp286
Jul 15, 2017

#1**0 **

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...

Answer and explination soon!!!

Trinityvamp286
Jul 15, 2017

#2**+1 **

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. :)

Melody
Jul 15, 2017