4400 Higher November 2008 Paper 3 Q16

EdexcelHigherOld spec6 marksCircle Theorems

16

Cyclic quadrilateral ABCD with diagonal AC and tangent PA at A; angle PAD = 54, angle ACB = 36 and angle ADC = 78 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on a circle.
\(PA\) is the tangent to the circle at \(A\).
Angle \(PAD = 54^\circ\), angle \(ACB = 36^\circ\) and angle \(ADC = 78^\circ\).

(a)
(i) Find the size of angle \(ACD\).
(ii) Give a reason for your answer.
(2)
(b) Explain why \(BD\) is a diameter of the circle. (2)
(c)
(i) Work out the size of angle \(ABC\).
(ii) Give a reason for your answer.
(2)
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