10.1 A double-headed rotating sprinkler (as shown in the picture below) is used to irrigate a circular vegetable garden - NSC Technical Mathematics - Question 10 - 2021 - Paper 2

To determine the length of chord ED, we will apply the Pythagorean theorem. The distance from O to the point where the tangent (chord EBD) meets the smaller circle is denoted as h, and the radius of the smaller circle is r = 4 m.

We first need to determine the height of the segment, which we calculated as:

$$h = 2.95 ext{ m}$$

Using the formula for the half-chord:

rac{ED}{2} = ext{sqrt}(r^2 - h^2)

In our case:

$$= 4 ext{ m} ext{ and } h = 2.95 ext{ m}\ ED = 2 imes ext{sqrt}(4^2 - 2.95^2)$$

Calculating this, we find:

$$$$

Thus, the length of chord ED is 5.40 m.