Geometry Questions with Solutions

7 questions4 easy2 medium1 hard

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.

All Questions Easy Medium Hard

Q1.
Let $M$ be a point inside the triangle $A B C$ . Then which one of the following is true?
A. $A B + A C < M B + M C$ B. $A B + A C > M B + M C$ C. $A B + A C \leq M B + M C$ D. None of these
easyAsked in NIMCET 2008View solution ›
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?
A. $1$ inchB. $2$ inchesC. $10$ inchesD. $23$ inches
hardAsked in NIMCET 2008View solution ›
Q3.
Each interior angle of a regular hexagon measures
A. $108^{\circ}$ B. $120^{\circ}$ C. $135^{\circ}$ D. $144^{\circ}$
easyView solution ›
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
A. 2 cmB. 3 cmC. 3.5 cmD. 6.75 cm
easyView solution ›
Q5.
The length of the tangent drawn from a point 13 cm away from the centre of a circle of radius 5 cm is
A. 8 cmB. 10 cmC. 12 cmD. 18 cm
easyView solution ›
Q6.
In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =
A. 1 : 3B. 3 : 1C. 2 : 1D. 1 : 2
mediumAsked in NIMCET 2019View solution ›
Q7.
The median AD of $△ A B C$ is bisected at E, and BE is extended to meet the side AC at F. Then AF : FC =
A. 1 : 3B. 2 : 1C. 1 : 2D. 3 : 1
mediumAsked in NIMCET 2019View solution ›