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Tangents from an external point: area of quadrilateral PAOB or the region they enclose

This type of question, asked 5 times: 2 May 2023 S2, 9 May 2024 S1, 25 Apr 2025 S1, 26 Apr 2025 S2, 19 Apr 2026 S2. All 5 questions 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

    25 Apr 2025 S1

    143
    A pair of tangents are drawn to the circle x2+y2+6x−4y−12=0x^{2}+y^{2}+ 6x- 4y- 12 = 0 from a point P(−4,−5)P( - 4, - 5), then the area enclosed between these tangents and the area of the circle is

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  4. Question 4

    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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  5. Question 5

    19 Apr 2026 S2

    56
    Let PA and PB be the tangent segments drawn from point P(6,8)P(6, 8) to the circle with the centre at origin O. The radius of circle for which the area of quadrilateral PAOB is maximum, is...

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