Higher June 2018 Paper 1 Q13

EdexcelHigherCurrent spec4 marksCircle Theorems

Circle with centre O; L, M and N are points on the circle; QMT is a tangent at M; lines LN, LM, NM, NO and OM are drawn; angle NLM = 27 degrees

Diagram NOT accurately drawn

\(L\), \(M\) and \(N\) are points on a circle, centre \(O\).
\(QMT\) is the tangent to the circle at \(M\).

(a)

(i) Find the size of angle \(NOM\).

(ii) Give a reason for your answer. (2)

(b)

(i) Find the size of angle \(NMQ\).

(ii) Give a reason for your answer. (2)

Mark scheme (a)

Scheme	Marks
(i) 54	B1
(ii) angle at centre is twice angle at circumference	B1
	(2)

Notes

B1: cao

B1: dep on B1 in (a)(i) accept alternative reasons
eg. angle at circumference is half the angle at the centre

Mark scheme (b)

Scheme	Marks
(i) 27	B1
(ii) alternate segment theorem	B1
	(2)
	(4 marks)

Notes

B1: ft from (a)(i) for \(\dfrac{\text{``}{54}\text{''}}{2}\)

B1: dep on B1 in (b)(i) accept alternative reason
angle between tangent and radius is 90°
If answer for (b)(i) is ft from (a)(i) then reason must be
angle between tangent and radius is 90°