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Ratio in which the intersection of two cevians of a triangle divides one of them

This type of question, asked 3 times: 19 Apr 2025 S2, 26 Apr 2025 S2, 19 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S2

    105
    In triangle ABC , the point P divides BC internally in the ratio 3:43:4 and Q divides CA internally in the ratio 5:35:3. If AP and BQ intersect in a point GG, then GG divides APAP internally in the ratio

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  2. Question 2

    26 Apr 2025 S2

    140
    In this question figure, PP divides ACAC in the ratio 3:43:4 and Q divides BC in the ratio 4:34:3. Then M divides AQ in the ratio

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  3. Question 3

    19 May 2026 S2

    89
    In a triangle PQR, L and M are the points on QR and PR respectively such that QL=2LRQL = 2LR and PM=3MRPM = 3MR. Let S be the point of intersection of PL and QM; then S divides segment QM internally in the ratio ...

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