The circle defined by the equation (x − 4)^2 + (y – 4)^2 = 25 has its center at point (4, 4)
and includes point (7, 8) on the circle. This is shown in the figure above. What is the
area of the circle shown?
A) 5π
B) 10π
C) 16π
D) 25πHere’s How to Crack It
You want the area, so write down the formula for area of a circle: A = πr^2 . That means you need to
determine the radius of the circle. If you remember the circle formula from the previous chapter, you
simply need to recall that r^2 = 25 and just multiply by π to find the area. If not, you can find the distance
between (4, 4) and (7, 8) by drawing a right triangle. The triangle is a 3-4-5 right triangle, so the distance
between (4, 4) and (7, 8) (and thus the radius) is 5. If the radius is 5, then the area is π(5)^2 , or 25π. The
answer is (D).
Arcs and Sectors
Many circle questions on the SAT will not ask about the whole circle. Rather, you’ll be asked about arcs
or sectors. Both arcs and sectors are portions of a circle: arcs are portions of the circumference, and
sectors are portions of the area. Luckily, both arcs and sectors have the same relationship with the circle,
based on the central angle (the angle at the center of the circle which creates the arc or sector):