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Circumradius from the sides or an angle (a = 2R sin A)

This type of question, asked 3 times: 4 May 2023 S1, 12 May 2024 S1, 25 Apr 2025 S2. All 3 questions below, oldest first.

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  1. Question 1

    4 May 2023 S1

    150
    In △ABC\triangle ABC, with usual notations, if b=3b=3, c=8c=8, m∠A=60∘m\angle A=60^\circ, then the circumradius of the triangle is ___ units.

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  2. Question 2

    12 May 2024 S1

    141
    In a triangle, the sum of lengths of two sides is xx and the product of the lengths of the same two sides is yy. If x2−c2=yx^{2}-c^{2}=y where cc is the length of the third side of the triangle, then the circumradius of the triangle is

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  3. Question 3

    25 Apr 2025 S2

    146
    The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is

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