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Angle bisector theorem: the bisector divides the opposite side in the ratio of the other two sides

This type of question, asked 2 times: 18 Jul 2023 S3, 12 Sep 2024 S2. All 2 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S3

    65
    If in △XYZ\triangle XYZ, XY = 4 and XZ = 5 cm, and Q is a point on YZ such that XQ bisects ∠X\angle X, then YQ : QZ is:

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  2. Question 2

    12 Sep 2024 S2

    54
    In ΔDEF\Delta DEF, the bisector of ∠D\angle D intersects side EF at point N. If DE = 36 cm, DF = 40 cm and EF = 38 cm, then the length (in cm) of NF is ________.

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