4400 Higher June 2009 Paper 3 Q9

EdexcelHigherOld spec4 marksCircle Theorems Pythagoras

Circle centre O with radius OA = 4.7 cm, tangent AB = 5.9 cm at A, and OB crossing the circle at C

Diagram NOT accurately drawn

\(A\) is a point on a circle with centre \(O\) and radius 4.7 cm.
\(AB\) is the tangent to the circle at \(A\).
\(AB = 5.9\) cm.
\(OB\) intersects the circle at \(C\).

Calculate the length of \(BC\).
Give your answer correct to 3 significant figures.

(4)

Mark scheme

Scheme	Marks
\(4.7^2 + 5.9^2\) \(= 22.09 + 34.81 = 56.9\)	M1
\(\sqrt{4.7^2 + 5.9^2}\)	M1
7.5432...	A1
2.84	A1
	(4)
	(4 marks)

Notes

M1: for squaring & adding

M1: (dep) for square root

A1: for value which rounds to 7.54

A1: for answer which rounds to 2.84 (2.84320...)