4MA0 Higher January 2014 Paper 4R Q14

EdexcelHigherOld spec5 marksCircle Theorems

14

Circle centre O with points A, B, C and D on the circle and tangent AE at A; angle ADC = 68 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\).
\(AE\) is a tangent to the circle.
Angle \(ADC = 68^\circ\)

(a)
(i) Find the size of angle \(ABC\).
(ii) Give a reason for your answer.
(2)
(b)
(i) Find the size of angle \(AOC\).
(ii) Give a reason for your answer.
(2)
(c) Find the size of angle \(CAE\). (1)
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