A, B, C and D are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 8 - 2018 - Paper 1

Applying the sine rule in triangle BOD:

rac{BD}{ ext{sin}( ext{angle BOD})} = rac{CD}{ ext{sin}( ext{angle CBD})}

We know that BD is the diameter, so BD = 2r, where r is the radius.

Next, we find angle BOD:

$$ext{angle BOD} = 180° - ext{angle CAD} = 180° - 28° = 152°.$$

Substituting values into the sine rule:

rac{2r}{ ext{sin}(152°)} = rac{6.4}{ ext{sin}(14°)}

Thus:

2r = rac{6.4 imes ext{sin}(152°)}{ ext{sin}(14°)}.

Calculating the right-hand side:

1. Calculate sin(14°) and sin(152°).
2. Substitute to find the value of r:

After performing the calculations, we will find:

r = rac{6.4 imes ext{sin}(152°)}{2 imes ext{sin}(14°)}.

Finally, use the area formula for a circle:

$$ext{Area} = ext{pi} imes r^2.$$

Insert the value of r calculated previously to find the area. Ensure to express the area in square centimeters.