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Find an angle from a relation among the sides using the cosine rule

This type of question, asked 5 times: 2 May 2023 S1, 22 Apr 2025 S1, 26 Apr 2025 S1, 18 Apr 2026 S1, 19 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    117
    In △ABC\triangle ABC, with usual notations, if 1b+c+1c+a=3a+b+c\dfrac{1}{b+c} + \dfrac{1}{c+a} = \dfrac{3}{a+b+c}, then m∠Cm\angle C is equal to

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  2. Question 2

    22 Apr 2025 S1

    108
    In △ABC\bigtriangleup ABC, with usual notations, if a4+b4+c4−2a2c2−2c2b2=0a^{4}+b^{4}+c^{4}- 2a^{2}c^{2}- 2c^{2}b^{2}= 0, then ∠C=…\angle C= \ldots.

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  3. Question 3

    26 Apr 2025 S1

    121
    In a triangle ABC , with usual notations, (a+b+c)(a+b−c)=3ab(a + b + c)(a + b - c) = 3ab, then ∠C=\angle C =

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  4. Question 4

    18 Apr 2026 S1

    63
    In triangle ABC, with usual notations, if (a+b+c)(a+b−c)=ab(a + b + c)(a + b - c) = ab, then the measure of angle C is...

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  5. Question 5

    19 Apr 2026 S2

    63
    In △ABC\triangle ABC, with usual notations, (a+b+c)(b+c−a)(c+a−b)(a+b−c)=3b2c2(a + b + c)(b + c - a)(c + a - b)(a + b - c) = 3b^2c^2, then ∠A=\angle A =

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