Higher June 2024 Paper 1 Q22
22 \(A\), \(B\) and \(C\) are points on a circle, centre \(O\).
\(AP\) and \(BP\) are tangents to the circle.
Not drawn accurately
Work out the size of angle \(x\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: drawing \(AO\) and \(BO\) and sum of angles in a quadrilateral | ||
| \(PBO = 90\) or \(PAO = 90\) | M1 | may be seen on diagram or implied by subsequent working accept rectangle drawn at angle |
| \(360 - 90 - 90 - 24\) or 156 | M1dep | oe eg \(180 - 24\) or \(90 - 12\) may be seen on diagram |
| 78 | A1 | |
| Alternative method 2: drawing \(AO\) and \(BO\) and using circle theorems | ||
| \(AOB = 2x\) | M1 | may be seen on diagram |
| \(2x = 156\) | M1dep | |
| 78 | A1 | |
| Alternative method 3: drawing \(AB\), sum of angles in a triangle and alt segment | ||
| \(2PAB + 24 = 180\) or \(2PBA + 24 = 180\) | M1 | |
| \((180 - 24) \div 2\) or 78 or \((180 - 24) \div 2\) or 78 | M1dep | may be seen on diagram |
| \(x = 78\) | A1 | |
| Alternative method 4: drawing \(PO\) and \(AO\) or \(BO\) and sum of angles in a triangle | ||
| \(PBO = 90\) or \(PAO = 90\) | M1 | may be seen on diagram or implied by subsequent working accept rectangle drawn at angle |
| \(180 - 90 - 12\) or 78 | M1dep | oe eg \(90 - 12\) may be seen on diagram |
| 78 | A1 | |
Additional guidance
| Answer 78 | M1M1A1 |
| Working takes precedence over diagram |