The diagram shows a circle, centre O - OCR - GCSE Maths - Question 16 - 2020 - Paper 6

Given that the radius of the circle is 8 cm, the diameter AOB is:

$AB = 2 \times 8 = 16 \: \text{cm}$

To find length BC, we can apply the tangent-secant theorem and the properties of triangles in the circle. The angle CAE is 32°, and angle ACB is 90°.

Using the sine rule in triangle ABC, we have:

$\frac{BC}{\sin(32°)} = \frac{AB}{\sin(90°)}$

Substituting AB:

$BC = AB \times \sin(32°) = 16 \times \sin(32°)$

Calculating this gives:

$\sin(32°) \approx 0.5299$

Thus,

$BC \approx 16 \times 0.5299 \approx 8.4784 \: \text{cm}$

Therefore, rounding this to two decimal places, the length BC is approximately:

$BC \approx 8.48 \: \text{cm}$