You play darts with a friend. the board is a circle with a 6-inch radius. the “bull’s eye” is a smaller circle in the center of the board with an 0.25-inch radius. you throw darts (small metal arrows) at the board. at the end of six weeks, she has thrown 500 darts. she hit the board every time and hit the bull’s eye 1 time if you throw 500 darts, how many times should you expect to hit the bull’s eye by random chance? compare this result to your friend’s result. is she a skilled player for hitting the bull’s eye or is the result of hers expected?

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)