Hint

Use the stated units and precision. Use the centre-angle theorem with C on the major arc.

Worked solution

(a)

Use the centre-angle theorem with C on the major arc.

The same chord gives twice the circumference angle: 90°.

Answer: \(90\)

(b)

Use \(\displaystyle OA=OB\) and the triangle angle sum.

In isosceles triangle AOB, each base angle is \(\displaystyle \frac{180- 90}{2}= 45\)°.

Answer: \(45\)

(c)

Use the tangent-chord theorem with the appropriate acute angle.

The alternate-segment angle equals ACB=45°.

Answer: \(45\)

Maths4U indicative marking guidance

Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.

(a) · 2 marks

• 1 mark: Use the centre-angle theorem with C on the major arc.
• 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.

Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.

Common error: Keep intermediate values exact until the final step.

(b) · 2 marks

• 1 mark: Use \(\displaystyle OA=OB\) and the triangle angle sum.
• 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.

Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.

Common error: Check the answer against the original conditions.

(c) · 2 marks

• 1 mark: Use the tangent-chord theorem with the appropriate acute angle.
• 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.

Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.

Common error: Keep intermediate values exact until the final step.

Total: 6 marks.