4400 Higher June 2009 Paper 3 Q14

EdexcelHigherOld spec5 marksCircle Theorems

14

Circle through A, B, C and D; tangent AT at A; DCE parallel to AT; ABE a straight line; angle BAD = 56 degrees and angle EAT = 47 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on a circle.
\(ABE\) and \(DCE\) are straight lines.
\(AT\) is a tangent to the circle.
\(DCE\) is parallel to \(AT\).
Angle \(EAT = 47^\circ\). Angle \(BAD = 56^\circ\).

(a)
(i) Find the size of angle \(AED\).
(ii) Give a reason for your answer.
(2)
(b) Find the size of angle \(BCD\). (1)
(c)
(i) Find the size of angle \(ADB\).
(ii) Give a reason for your answer.
(2)
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