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2026 CCHMS P2 Q5
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2026 CCHMS P2 Q5
Secondary 4
12 marks
\(PQRS\) is a trapezium where \(PS\) is parallel to \(QR\).
\(QS\) intersects \(PR\) at \(T\).
Angle \(TQR=\) angle \(QRT\).
Show that triangles \(PQT\) and \(SRT\) are congruent.
[5]
In the diagram, \(A,B,C,D\) are points on a circle, centre \(O\).
The tangents at \(A\) and \(B\) meet at \(T\).
Angle \(ATB=40^\circ\) and angle \(BCD=95^\circ\).
Find, giving reasons for each step of your working,
angle \(BOA\),
[2]
angle \(ACB\),
[2]
angle \(OAD\).
[3]
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Answer:
(a) \(TP=TS\), \(TQ=TR\), included vertically opposite angles equal: SAS. (b)(i) \(140^\circ\) (ii) \(70^\circ\) (iii) \(65^\circ\).
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