Higher January 2022 Paper 2 Q16

EdexcelHigherCurrent spec4 marksCircle Theorems

16 \(D\), \(E\), \(F\) and \(G\) are points on a circle, centre \(O\)

Circle with centre O and points D, E, F and G on the circumference; EOG is a straight line through O, and chords DG, DE, DF, EF and FG are drawn; angle EGD is marked 42 degrees

Diagram NOT accurately drawn

\(EOG\) is a diameter of the circle.
Angle \(EGD = 42°\)

Calculate the size of angle \(DFG\)
Give a reason for each stage of your working.

(4)

Mark scheme

Scheme	Marks
\(DFE = 42°\) or \(DOG = 180 - 2 \times 42\;(= 96)\) or \(EFG = 90°\) or \(EDG = 90°\) or \(DEG = 90 - 42\;(= 48)\)	M1
48°	A1
angles in same segment or angles from same chord or angles at the circumference subtended from the same arc of the circle angles in a semicircle are 90° angles in a semicircle are 90° angle subtended by diameter is 90° angle at centre twice angle at circumference oe angles in a triangle add to 180 angles in a triangle add to 180	B2
	(4)
	(4 marks)

Notes

M1: used or seen in diagram (must be clearly labelled if not in diagram)

A1: award 2 marks for 48 unless from an incorrect method

B2: Dep on a fully correct method to find angle \(DFG\) for a full set of reasons relevant to their method.
B1 dep on M1 for at least one relevant circle theorem.