NIMCET 2008
Let be a point inside the triangle . Then which one of the following is true?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B —
Detailed Solution
Extend to meet at .
In : .
In : . Adding and cancelling : , i.e. .
✓ Check
Equilateral triangle of side with at the centroid: .⚠ Common trap
Option (A) reverses the inequality, thinking the bent path through is longer; the centroid example gives .Quick tip
Extend to and use the triangle inequality twice
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Geometry — Preparation
This question tests your understanding of Geometry, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Geometry in entrance exams covers lines and angles, triangles, quadrilaterals, polygons and circles. Questions test properties of angles formed by parallel lines, congruence and similarity of triangles, the Pythagorean theorem, properties of special quadrilaterals, interior and exterior angles of polygons, and circle theorems such as angles in the same segment and tangent properties. Most geometry questions are solved by recognising the right property, not by long calculation. A neat rough diagram, labelled with the given information, often reveals the answer. Pythagorean triplets (3-4-5, 5-12-13, 8-15-17) and the 30-60-90 and 45-45-90 triangle ratios are worth memorising because they appear repeatedly. Practise the geometry questions below. Each comes with a step-by-step solution that names the property used.