2026 PHS P2 Q9

2026 PHS P2 Q9

Secondary 4
11 marks
  1. In the diagram, \(ABC\) is a triangle where \(AB=AC\) and \(M\) is the midpoint of \(BC\).
    \(XY\) is perpendicular to \(AC\).
    1. Show that triangles \(ACM\) and \(XCY\) are geometrically similar.[2]
    2. \(AB=20\text{ cm}\), \(XY=5\text{ cm}\) and angle \(XCY=30^\circ\).
      Find the value of \(\dfrac{\text{area of}\hspace{0.5em}\triangle XCY}{\text{area of}\hspace{0.5em}\triangle ABC}\).[3]
  2. \(ABCDEFGH\) is part of a regular \(n\)-sided polygon.
    Each exterior angle of the polygon is \(2x^\circ\) and each interior angle is \(13x^\circ\).
    \(ABP\) and \(HGP\) are straight lines.
    1. Find the size of each interior angle of the \(n\)-sided polygon.[2]
    2. Find the size of angle \(BPG\).[4]

Solution:

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Answer:(a)(i) \(\triangle ACM\sim\triangle XCY\) (AA) (ii) \(\dfrac18\) (b)(i) \(156^\circ\) (ii) \(36^\circ\)

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