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DE parallel to BC cuts off a similar triangle: areas of the parts

This type of question, asked 4 times: 18 Jul 2023 S3, 20 Jul 2023 S4, 24 Jul 2023 S4, 15 Sep 2025 S1. All 4 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S3

    52
    D and E are points on the sides AB and AC, respectively, of ΔABC\Delta ABC such that DE is parallel to BC and AD : DB = 7 : 9. If CD and BE intersect each other at F, then find the ratio of areas of ΔDEF\Delta DEF and ΔCBF\Delta CBF

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  2. Question 2

    20 Jul 2023 S4

    61
    In a ΔABC\Delta ABC, DE ∥\parallel BC, where D is a point on AB and E is a point on AC. If DE divides the area of ΔABC\Delta ABC into two equal parts, then DB : AB is equal to:

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  3. Question 3

    24 Jul 2023 S4

    71
    In the given ΔABC\Delta ABC, DE ∥\parallel BC. If BC = 8 cm, DE = 6 cm and area of ΔADE=90 cm2\Delta ADE = 90\ \text{cm}^2, then what is the area of ΔABC\Delta ABC (in cm2\text{cm}^2)?

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  4. Question 4

    15 Sep 2025 S1

    70
    In △ABC\triangle ABC, a line segment DE is parallel to BC, with D on AB and E on AC. If the ratio of the area of △ADE\triangle ADE to the area of the trapezoid DECB is 4:21, what is the ratio of AD to DB?

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