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Angle subtended by a chord at a point on the minor arc and at the centre

This type of question, asked 2 times: CDS 2 2018, CDS 1 2026. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    84
    The chord of a circle is 3\sqrt{3} times its radius. The angle subtended by this chord at the minor arc is k times the angle subtended at the major arc. What is the value of k ?

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  2. Question 2

    CDS 1 2026

    52
    Let O be the centre of a circle. Let A, B and C lie on the circle such that ∠ABC=153∘\angle ABC = 153^\circ. What is the value of ∠AOC\angle AOC ?

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