2025 IGCSE 0580 February/March P22 Q14

2025 IGCSE 0580 February/March P22 Q14

5 marks

\(A,B,C,D\) and \(E\) lie on a circle.

\(FG\) is a tangent to the circle at \(C\).

Angle \(BAD=110^\circ\), angle \(ADB=20^\circ\) and angle \(BEC=45^\circ\).

  1. Find angle \(BCD\).
    Give a geometrical reason for your answer.[2]
    1. Find angle \(DBC\).[2]
    2. Find angle \(DCG\).[1]

Solution:

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Answer:(a) \(70^\circ\); opposite angles of a cyclic quadrilateral sum to \(180^\circ\). (b)(i) \(65^\circ\). (ii) \(65^\circ\).

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