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Angle bisector theorem BD/DC = AB/AC: find a side or segment

This type of question, asked 5 times: CDS 2 2020, CDS 1 2022, CDS 1 2025, CDS 1 2026, CDS 2 2026. All 7 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    62
    In a △ABC\triangle ABC, AC = 12 cm, AB = 16 cm and AD is the bisector of ∠A\angle A. If BD = 4 cm, then what is DC equal to ?

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  2. Question 2

    CDS 1 2022

    87
    In a triangle ABCABC, ADAD is the bisector of ∠BAC\angle BAC. If AB=12AB = 12 cm, BD=10BD = 10 cm and DC=5DC = 5 cm, then what is the perimeter of the triangle?

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  3. Question 3

    CDS 1 2022

    81
    In a triangle ABCABC, AB=16AB = 16 cm, AC=12AC = 12 cm and ADAD is the bisector of ∠A\angle A. If BD=4BD = 4 cm, then what is CDCD equal to?

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  4. Question 4

    CDS 1 2025

    14
    In a triangle ABC, AB = 2 cm, BC = 4 cm and AC = 3 cm. The bisector of angle A meets BC at D and the bisector of angle B meets AD at E. What is AE : ED equal to ?

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  5. Question 5

    CDS 1 2025

    15
    In a triangle ABC, the bisector of angle A cuts BC at D. If AB + AC = 10 cm and BD : DC = 3 : 1, then what is the length of AC ?

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  6. Question 6

    CDS 1 2026

    68
    In a triangle ABC, AB = 18 cm, BC = 22 cm and AC = 15 cm. The bisector of ∠BAC\angle BAC intersects BC at D. What is (BD ×\times DC) equal to ?

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  7. Question 7

    CDS 2 2026

    74
    In a triangle ABC, AD is the bisector of angle A that meets BC at D. If AB = 21 cm, DC = 20 cm and AB : AC = 3 : 4, then what is AC2−BD2AC^2 - BD^2 equal to ?

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