4400 Higher November 2004 Paper 3 Q12

EdexcelHigherOld spec6 marksCircle Theorems

12 \(A\), \(B\), \(C\) and \(D\) are points on a circle.
Angle \(BAC = 40^\circ\).
Angle \(DBC = 55^\circ\).

Cyclic quadrilateral ABCD with diagonals AC and BD; angle BAC = 40 degrees, angle DBC = 55 degrees

Diagram NOT accurately drawn

(a)
(i) Find the size of angle \(DAC\).
(ii) Give a reason for your answer. (2)
(b)
(i) Calculate the size of angle \(DCB\).
(ii) Give reasons for your answer. (3)
(c) Is \(BD\) a diameter of the circle?
Give a reason for your answer. (1)
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