Consider a triangle with sides , and . Choose a random point inside the triangle. The minimum distances from to , and are , and respectively. Find .
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4 marks, −1MathematicsCoordinate and solid geometryAreas, polygons and the Pythagorean theoremModerateabout 2 min
DSE 2021 Question 12: Coordinate and solid geometry
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Plain-text version
Consider a triangle with sides AC = 2, AB = √3 and BC = 1. Choose a random point P inside the triangle. The minimum distances from P to AC, AB and BC are D₁, D₂ and D₃ respectively. Find 2D₁ + √3D₂ + D₃. (A) √3 (B) 3 + √3 (C) 3√3 (D) 3 - √3
Also written as: Consider a triangle with sides AC = 2, AB = sqrt(3) and BC = 1. Choose a random point P inside the triangle. The minimum distances from P to AC, AB and BC are D_1, D_2 and D_3 respectively. Find 2D_1 + sqrt(3)D_2 + D_3.
Coordinate and solid geometry has come up 18 times in 2 exams since 2008.
What this question tests
This question is on Areas, polygons and the Pythagorean theorem, part of Coordinate and solid geometry in Mathematics.
Areas of plane figures and right-angle distances.
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Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.