A soccer ball has diameter of 400 mm. A pin is stuck into the ball such that it creates the chord AC, which is 20 mm. What is the distance from the chord formed by the pin, and what is the length of EB? (Hint: CD=radius)
To find the distance from the chord formed by the pin, we need to find the distance between the midpoint of the chord and the center of the soccer ball. Let's call the center of the soccer ball point O.
1. Begin by drawing a diagram with the soccer ball, the chord AC, and the point O as the center of the soccer ball.
2. Since the chord AC is perpendicular to the diameter, we can draw a line segment OD from the center of the ball to the midpoint of the chord AC.
3. The length of the chord AC is given as 20 mm, which means OD is half of that, or 10 mm.
4. Now, we need to find the length of the line segment OE, which is the distance between the chord AC and the center O of the soccer ball.
5. Since CD is the radius of the soccer ball, it is half the diameter, so it is 400 mm / 2 = 200 mm.
6. To find OE, we can use the Pythagorean theorem. We have OD = 10 mm (from step 3) and CD = 200 mm (from step 5).
Using the Pythagorean theorem, we have:
OE^2 = OD^2 + DE^2
Solving for DE, we have:
DE^2 = OE^2 - OD^2
7. From the diagram, we can see that DE is a straight line connecting the midpoint of the chord AC with the center O of the soccer ball.
8. Since DE is perpendicular to AC, it creates right triangle ODE. Therefore, DE^2 + OD^2 = OE^2.
9. Substitute the known values:
DE^2 = OE^2 - OD^2
DE^2 = OE^2 - 10^2
10. To find the length of EB, notice that EB is half the length of AC, so EB is 20 mm / 2 = 10 mm.