Specimen 2020 Paper 1 Q9
9 \(A\), \(B\), \(C\) and \(D\) are points on a circle.
\(\angle BCA = x \qquad \angle ACD = 2x \qquad \angle CAD = 3x \qquad \angle CAB = 4x\)
Not drawn accurately
Prove that \(AC\) is a diameter. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x + 2x + 3x + 4x = 180\) or \(10x = 180\) | M1 | oe |
| \(x = 18\) or \(5x = 90\) | M1dep | must see working for first M1 |
| \(\angle ABC = 90\) or \(\angle ADC = 90\) and (converse of) angle in a semicircle and \(AC\) is a diameter | A1 | must see working for M1M1 |
| (sum of) opposite angles of a cyclic quad = 180 and angle sum of a triangle = 180 | A1 | must see working for M1M1 |
Additional guidance
The final A1 is likely to be seen within the working for M1M1A1