Higher June 2024 Paper 1R Q13

EdexcelHigherCurrent spec5 marksCircle Theorems

Circle centre O with points A, B, C and D on the circle; lines AB, BC, CD, DA, OB and OD drawn; angle BCD = 128 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\)

Angle \(BCD = 128^\circ\)

Work out the size of angle \(OBD\)
Give a reason for each stage of your working.

(5)

Mark scheme

Scheme	Marks
\(BAD\) = 180 – 128 (= 52) or (reflex) \(BOD\) = 2 × 128 (= 256)	M1
(obtuse) \(BOD\) = 2 × “52” (= 104) or (obtuse) \(BOD\) = 360 – “256” (= 104)	M1
Correct answer of 38 scores 3 marks (unless from obvious incorrect working) Answer: 38	A1
	B2
	(5)
	(5 marks)

Notes

M1: angles to be identified either by notation or correctly positioned on the diagram.

M1: (dep on M1) angles to be identified either by notation or correctly positioned on the diagram.

B2: dep on a fully correct method to find \(OBD\) for correct reasons for method used.

(B1 dep on M1 for a correct circle theorem for their method)

Opposite angles of a cyclic quadrilateral sum to 180°
Angle at the centre is 2 × (double) angle at circumference / angle at circumference is ½ angle at centre

Angles around a point add up to 360°
Isosceles triangle
Angles in a triangle add to 180°
Angles in a triangle add to 180°