Latest Challenge

10 August, 2025

Figure 1

Let \(ABCD\) be a trapezium with \(AB \parallel CD\) and diagonals \(AC\) and \(BD\) intersecting at \(O\). The areas of the triangles \(\triangle AOB\), \(\triangle BOC\), \(\triangle COD\), and \(\triangle AOD\) are all integers.

It is known that the products of the areas of two pairs of these triangles are \(576\) and \(1296\), respectively.

Note: \(AD\) and \(BC\) might not be equal, unlike what one might infer from the image.

Submission: Google forms

Deadline: 17 August, 2025.

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