4MA0 Higher June 2017 Paper 3R Q17 – Westie's Workshop

4MA0 Higher June 2017 Paper 3R Q17

EdexcelHigherOld spec3 marksCircle Theorems

17

Circle through C, B, X and Y; straight line AXY with AX = 12 cm and XY = 6 cm, straight line ABC with AB = 9 cm; A outside the circle

Diagram NOT accurately drawn

The points \(B\), \(C\), \(Y\) and \(X\) lie on a circle.
\(AXY\) and \(ABC\) are straight lines.

\(AX = 12\) cm \(\qquad XY = 6\) cm \(\qquad AB = 9\) cm

Calculate the length of \(BC\).

(3)

Mark scheme

Scheme	Marks
12 × (12+ 6) = 9 × (9 + \(BC\)) oe or 12 × (12+ 6) = 9 × \(AC\) oe or \(AC = 24\)	M1
(\(BC =\)) \(\dfrac{12 \times (12 + 6)}{9} - 9\) oe or 24 – 9	M1
15	A1
	(3)
	(3 marks)

Notes

M1: for a complete method

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