Final answer:
The approximate length of the chord along the circle that touches the smaller circle is 7.75 cm.
Step-by-step explanation:
To construct the area of a circle with a radius of 5cm and 3cm, we can calculate the length of the chord along a circle that touches the smaller circle. The length of the chord can be found using the formula:
Length of chord = 2 * square root of (radius of larger circle * radius of smaller circle)
For the given radius of 5cm and 3cm, we have:
Length of chord = 2 * square root of (5 * 3) = 2 * square root of 15
Using a calculator, we can approximate the value to:
Length of chord ≈ 7.75 cm.
Therefore, none of the given answer choices (a) 6 cm, (b) 8 cm, (c) 10 cm, or (d) 12 cm, is correct. The approximate length of the chord along the circle that touches the smaller circle is 7.75 cm.