4MA0 Higher January 2017 Paper 4 Q13

EdexcelHigherOld spec3 marksCircle Theorems

Circle with centre O and points B, D and E on it; tangent ABC touches the circle at B; DEC is a straight line; angle ABD = 79 degrees and angle ECB = 41 degrees

Diagram NOT accurately drawn

\(B\), \(D\) and \(E\) are points on a circle, centre \(O\).
\(ABC\) is a tangent to the circle.
\(DEC\) is a straight line.
Angle \(ABD = 79^\circ\) and angle \(ECB = 41^\circ\)

(a) Write down the size of angle \(BED\). (1)

(b) Work out the size of angle \(BOE\). (2)

Scheme	Marks
79°	B1
	(1)

Scheme	Marks
\(\angle BDE = 79 - 41\) or 180 − 101 − 41(= 38) or \(\angle OBE = 90 - 38\) or 90 − (180 − 101 − 41) (=52)	M1
76	A1
	(2)
	(3 marks)

Notes