NIMCET 2019
The median AD of is bisected at E, and BE is extended to meet the side AC at F. Then AF : FC =
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — 1 : 2
Detailed Solution
Draw meeting AC at G. In , D is the midpoint of BC, so G is the midpoint of FC: .
In , E is the midpoint of AD and , so F is the midpoint of AG: .
, so .
✓ Check
Mass points: masses 1 at B and C give 2 at D; E is the midpoint of AD, so A also has mass 2; on AC, (mass at C : mass at A).⚠ Common trap
(B) 2 : 1 is FC : AF, the ratio reversed.
Quick tip
Midpoint theorem twice:
💬 Discussions on this question
Ask a doubt ›Still stuck on this question? Ask our faculty and fellow students — answers appear here.
Ask a doubtMore Geometry Questions
View all ›- Q1.Let be a point inside the triangle . Then which one of the following is true?
- Q2.What is the diameter of the largest circle that can be drawn on a chessboard so that its entire circumference gets covered by the black squares and no part of the circumference falls on any white space, given that the chessboard has black and white squares of side one inch?
- Q3.Each interior angle of a regular hexagon measures
- Q4.In triangle ABC, D and E are points on AB and AC such that DE ∥ BC. If AD = 3 cm, DB = 2 cm and AE = 4.5 cm, then EC is
- Q5.The length of the tangent drawn from a point 13 cm away from the centre of a circle of radius 5 cm is
More Quantitative Aptitude Questions
- Q1.By selling 45 lemons for ₹40, a man loses 20%. How many lemons should he sell for ₹24 to gain 20%?Profit, Loss & Discount
- Q2.The marked price of an article is 1.45 times its cost price. Its selling price is ₹1,500 and the profit is 25%. What is the discount percentage? Profit, Loss & Discount
- Q3.Let A be a real number. Then the roots of the equation are real and distinct if and only if Quadratic Equations
- Q4.The number of distinct real roots of the equation is Quadratic Equations
- Q5.The roots of are:Quadratic Equations
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.