4MA0 Higher June 2017 Paper 4R Q15

EdexcelHigherOld spec4 marksCircle Theorems

15

Cyclic quadrilateral ABCD with diagonal AC; EDF is the tangent at D, with angle ADE = 61 degrees and angle CDF = 53 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on a circle.
\(EDF\) is the tangent to the circle at \(D\).
Angle \(ADE = 61^\circ\) and angle \(CDF = 53^\circ\)

(a)
(i) Write down the size of angle \(ACD\).
(ii) Give a reason for your answer. (2)
(b) Work out the size of angle \(ABC\). (2)
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