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Angle bisector meets the opposite side: length of one segment (bisector theorem)

The same question, asked 2 times: 15 Nov 2020 Tier II*, 3 Feb 2022 Tier II. Every wording below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    64
    In Δ\DeltaABC, the bisector of ∠\angleA intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, then the length of BD is:

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  2. Question 2

    3 Feb 2022 Tier II

    77
    In △PQR\triangle PQR, the bisector of ∠R\angle R meets side PQ at S, PR = 10 cm, RQ = 14 cm and PQ = 12 cm. What is the length of SQ?

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