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Point where the tangents at the ends of a chord of a circle meet

This type of question, asked 2 times: 29 Jul 2022, 29 Jan 2023. All 3 questions below, oldest first.

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  1. Question 1

    29 Jul 2022

    178
    Let ABAB be a chord of length 12 of the circle (x−2)2+(y+1)2=1694(x - 2)^{2}+ (y + 1)^{2}=\frac{169}{4}. If tangents drawn to the circle at points AA and BB intersect at the point PP, then five times the distance of point PP from chord ABAB is equal to

  2. Question 2

    29 Jan 2023

    77
    Let the tangents at the points A(4,−11)A(4, - 11) and B(8,−5)B(8, - 5) on the circle x2+y2−3x+10y−15=0x^{2}+y^{2}- 3x + 10y - 15 = 0, intersect at the point CC. Then the radius of the circle, whose centre is CC and the line joining AA and BB is its tangent, is equal to

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  3. Question 3

    29 Jan 2023

    179
    A circle with centre (2,3)(2,3) and radius 4 intersects the line x+y=3x + y = 3 at the points PP and QQ. If the tangents at PP and QQ intersect at the point S(α,β)S(\alpha,\beta), then 4α−7β4\alpha - 7\beta is equal to