2026 TPSS P2 Q5

2026 TPSS P2 Q5

Secondary 4
6 marks

In the diagram, \(O\) is the centre of the circle \(ABCD\). \(TBP\) and \(TDQ\) are tangents to the circle, angle \(BTD=36^\circ\) and \(AB=AD\).

Giving reasons for each step of your working, find

    1. angle \(BOD\),[2]
    2. angle \(ABD\).[2]
  2. Show that \(AB\) bisects angle \(UBD\).[2]

Solution:

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Answer:(a)(i) \(144^\circ\) (ii) \(36^\circ\) (b) \(\angle UBA=\angle ABD=36^\circ\), so \(AB\) bisects \(\angle UBD\).

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