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Triangles cut off by the diagonals are similar: area ratio = square of the side ratio

This type of question, asked 2 times: CDS 2 2017, CDS 1 2021. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2017

    64
    The diagonals of a cyclic quadrilateral ABCD intersect at P and the area of the triangle APB is 24 square cm. If AB = 8 cm and CD = 5 cm, then what is the area of the triangle CPD ?

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  2. Question 2

    CDS 1 2021

    89
    ABCDABCD is a trapezium in which ABAB is parallel to DCDC and 2AB=3DC2AB = 3DC. The diagonals ACAC and BDBD intersect at OO. What is the ratio of the area of △AOB\triangle AOB to that of △DOC\triangle DOC?

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