2026 PHS P1 Q21

2026 PHS P1 Q21

Secondary 4
4 marks

\(A\), \(B\), \(C\), \(D\) and \(E\) are points on the circle, centre \(O\).

\(AC\) is the diameter.

\(AC\) and \(ED\) are extended to meet at \(F\).

\(CE=CF\) and angle \(AFD=x^\circ\).

  1. Show that angle \(DBC=x^\circ\).
    Give a reason for each step of your working.[2]
  2. Find, in terms of \(x\), angle \(ACD\).
    Give a reason for each step of your working.[2]

Solution:

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Answer:(a) \(\angle DBC=x^\circ\) (shown) (b) \(90^\circ-x^\circ\)

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