Problem Solving

please explain each bit of details?

Since 30,40 are the points on the circle, the distance from the origin to the point on the circle will be the radius.

r^2 = 30^2 + 40^2

r = sqrt 2500

r = 50

area = pi r^2 = 50^2 pi = 2500 pi.

Hence D.

parallel_chase wrote:Since 30,40 are the points on the circle, the distance from the origin to the point on the circle will be the radius.

r^2 = 30^2 + 40^2

r = sqrt 2500

r = 50

area = pi r^2 = 50^2 pi = 2500 pi.

Hence D.

Good solution using the Pythagorean formula.

We can shave some time off if we quickly recognize a 3x:4x:5x triangle in the mix. 3/4/5 is the most commonly tested Pythagorean triplet and almost always shows up in some form on test day.

As soon as you see that you have a 30/40/x right angle triangle, 50 should come to mind as the radius. Then calculate the area as above.

Other important triplets to know:

5x:12x:13x
x:x:xroot2 (right isosceles triangle)
x:xroot3:2x (30/60/90 triangle)

and less tested, but still comes up:

7x:24x:25x

(D)