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Area of the quadrilateral formed by two tangents from P and the radii to their points of contact

The same question, asked 3 times: 2 May 2023 S2*, 9 May 2024 S1, 26 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S2

    101
    Two tangents drawn from P(1,7)P(1,7) to the circle x2+y2=25x^2 + y^2 = 25, touch the circle at Q and R respectively. The area of the quadrilateral PQOR is

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  2. Question 2

    9 May 2024 S1

    120
    Two tangents to the circle x2+y2=4x^2+y^2=4 at the points A and B meet at the point P(−4,0)P(-4,0). Then the area of the quadrilateral PAOBPAOB, O being the origin, is

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  3. Question 3

    26 Apr 2025 S2

    130
    Two tangents to the circle x2+y2=4x^{2}+y^{2}= 4 at the points A and B meet at P(−4,0)P( - 4,0). Then the area of quadrilateral PAOB, where ' O ' is the origin is

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