4MA0 Higher June 2015 Paper 3 Q21

EdexcelHigherOld spec3 marksCircle Theorems

Circle with diameter CA extended to D; DB is a tangent at B; angle BAC = 32 degrees

Diagram NOT accurately drawn

\(A\), \(B\) and \(C\) are three points on a circle.
\(DCA\) is a straight line.
\(CA\) is a diameter of the circle.
\(DB\) is a tangent to the circle.

Calculate the size of angle \(CDB\).

(3)

Mark scheme

Scheme	Marks
Angle \(CBD = 32^\circ\) or angle \(ABC = 90^\circ\) or angle \(DBO = 90^\circ\) or angle \(OBA = 32^\circ\) or angle \(BOD = 2 \times 32\) (= 64) (where \(O\) is the centre of the circle)	M1
eg (Angle \(BDC\) =) \(180^\circ - 32^\circ - 32^\circ - 90^\circ\)	M1
26	A1
	(3)

Notes

M1: angle must be clearly identifed either on diagram or in working

M1: for a complete method