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MHT CET202519 Apr 2025Evening ShiftMathematicsVector AlgebraActual

In triangle ABC , the point P divides BC internally in the ratio 3: 4 and Q divides CA internally in the ratio 5: 3 . If AP and BQ intersect in a point G , then G divides A P internally in the ratio

Options

  1. A2: 1
  2. B5: 7
  3. C7: 5
  4. D1: 2

Correct answer

C. 7: 5

Step-by-step solution

Given triangle ABC with point P on BC dividing it 3:4 so BP:PC = 3:4 and point Q on CA dividing it 5:3 so CQ:QA = 5:3 , determine the ratio AG:GP using Menelaus’ Theorem. Apply Menelaus’ Theorem to ACP with transversal B-G-Q : AQ QC CB BP PG GA = 1 Substitute the given ratios: From CQ:QA = 5:3 , AQ QC = 3 5 From BP:PC = 3:4 , BC = BP + PC = 3k + 4k = 7k for some k , so CB BP = 7 3 Thus, ( 3 5 ) ( 7 3 ) PG GA = 1 7 5 PG GA = 1 PG GA = 5 7 Since AG GP = 7 5 , point G divides AP internally in the ratio 7:5 . Final ans

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