4MA0 Higher June 2012 Paper 3 Q15

EdexcelHigherOld spec4 marksBasic Trigonometry Circle Theorems

Circle centre O with diameter BOD, tangent AB at B, AO = 8 cm, angle BAO = 30 degrees and angle CBD = 63 degrees

Diagram NOT accurately drawn

\(B\), \(C\) and \(D\) are points on a circle, centre \(O\).
\(BOD\) is a diameter of the circle.
\(AB\) is the tangent to the circle at \(B\).
\(AO\) = 8 cm. Angle \(BAO = 30^\circ\) Angle \(CBD = 63^\circ\)

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

(4)

Mark scheme

Scheme	Marks
(\(OB\) =) 8 sin 30° or 4	M1
(\(BD\) =) 2 × “4” or 8	M1
A complete correct method eg (\(BC\) =) “8” cos 63°	M1
3.63	A1
	(Total 4 marks)

Notes

A1: for ans rounding to 3.63 (3.63192…)

Apart from Questions 9, 13, 18, 20 and 21 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.