June 2024 Paper 1 Q16
16 \(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\).
angle \(OBC\) : angle \(ODC = 5 : 3\)
Work out the size of angle \(OBC\).
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((BOD =)\ 104^\circ\) | B1 | |
| \((BCD =)\ 128^\circ\) | B1 | |
| \((OBC + ODC =)\) \(360^\circ -\) (their) \(128^\circ -\) (their) \(104^\circ\) or \(OBC + ODC = 128^\circ\) or \(128 = 8x\) | M1 | oe eg \(360^\circ - 232^\circ\) one of \(128^\circ\) and \(104^\circ\) must be correct this could imply B1 B1 oe |
| \((OBC =)\ 80^\circ\) | A1 | can only be awarded with evidence of B2M1 |
Additional guidance
| Angles may be seen on diagram | |
| Check they are not splitting \(BCD\) in the ratio 5:3 (benefit of doubt may need to be applied). It is possible to draw a line from \(O\) to \(C\) which splits the quadrilateral into two isosceles triangles. This method does allow for \(BCD\) to be split in the ratio 5:3 | |
| \(OBC = 80^\circ\) and \(ODC = 48^\circ\) both on answer line | A1 |
| \(80^\circ\) and \(48^\circ\) both on answer line would be choice | A0 |
| Condone other forms of angle notation |