Attachment:
Eye of the Tiger.jpg
If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded?
A. 3/16
B. 1/5
C. 6/25
D. 1/4
E. 3/8
Hi, I want to know why we don't get same answer using PQ = 2?
OE
[Reveal] Spoiler:
Let us say that line segment RT has a length of 1. RT is the radius of circle R, so circle R has a radius of 1.
Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2.
Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4.
The question is asking us what fraction of circle P is shaded. The answer will be
(shaded area) (area of circle P)
The area of circle P is (4)2, which equals 16. The shaded area is just the area of circle Q (i.e. (2)^2, which equals 4) minus the area of circle R (i.e. (1)^2, which equals ). Therefore, the answer to our question is
(4 - ) / 16
Line segment QT is the diameter of circle R, so it has a length of 2 (twice the radius of circle R). Segment QT also happens to be the radius of circle Q, which therefore has a radius of 2.
Line segment PT, being the diameter of circle Q, has a length of 4. Segment PT also happens to be the radius of circle P, which therefore has a radius of 4.
The question is asking us what fraction of circle P is shaded. The answer will be
(shaded area) (area of circle P)
The area of circle P is (4)2, which equals 16. The shaded area is just the area of circle Q (i.e. (2)^2, which equals 4) minus the area of circle R (i.e. (1)^2, which equals ). Therefore, the answer to our question is
(4 - ) / 16