2025 NASS PRELIMS P1 Q10

2025 NASS PRELIMS P1 Q10

Secondary 4
8 marks
2025 Ngee Ann Secondary School Prelims A Math Paper 1

In the diagram, \(A, B, C\) and \(D\) lie on a circle. The tangents to the circle at \(A\) and \(D\) meet at \(E\).

It is given that angle \(ACD =\) angle \(BDA\) and \(BA = AE\).

  1. Show, giving all reasons, that
    1. triangle \(ABD\) is isosceles,[2]
    2. triangle \(BDA\) and triangle \(ADE\) are congruent.[3]
  2. Given that \(BD\) is parallel to \(AE\), prove that \(ABDE\) is a rhombus.[3]

Solution:

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Answer:(a)(i) \(AB=AD\), so \(\triangle ABD\) is isosceles. (a)(ii) \(\triangle BDA\cong\triangle ADE\) by SSS, using \(BD=AD\), \(DA=DE\), and \(BA=AE\). (b) \(ABDE\) is a rhombus.

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