# Geometry Practice Questions

Angles, Triangles, Quadrilaterals, Circles, Semi circles and squares. A collection of curated practice questions on Geometry that typically appear in TANCET, GMAT, GRE, CAT and other B School admission tests. Detailed explanatory answers and shortcuts, wherever applicable, are provided for each of the questions.

What is the ratio measures of the in-radius, circum-radius and one of the ex-radius of an equilateral triangle?

- 1 : 2 : 5
- 1 : 3 : 5
- 1 : 2 : 3
- 1 : 1.4142 : 2

If in a triangle ABC, \\frac{cos A}{a}) = \\frac{cos B}{b}) = \\frac{cos C}{c}), then what can be said about the triangle?

- Right angled triangle
- Isosceles triangle
- Equilateral triangle
- Nothing can be inferred

If the largest angle in a triangle is 70

^{o}, what is least possible value of the smallest angle of the triangle?- 69
^{o} - 1
^{o} - 40
^{o} - 39
^{o} - 41
^{o}

- 69
If the shaded area is one half the area of triangle ABC and angle ABC is right angle, then the length of line segment AD is

- \\frac{1}{2})w
- c
- \\sqrt {{2x}^{2}+{z}^{2}})
- \\sqrt {{w}^{2}-{3y}^{2}})
- \\sqrt {{y}^{2}+{z}^{2}})

Which of the following is incorrect?

- An incentre is a point where the angle bisectors meet.
- The median of any side of a triangle bisects the side at right angle.
- The point at which the three altitudes of a triangle meet is the orthocentre
- The point at which the three perpendicular bisectors meet is the centre of the circumcircle.

A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?

- 75% of the of the original square
- 50% of the size of the original square
- 75% of the size of the circle
- 25% of the size of the original square

What is the area of the largest triangle that can be fitted into a rectangle of length 'l' units and width 'w' units?

- \\frac{lw}{3})
- \\frac{2lw}{3})
- \\frac{3lw}{4})
- \\frac{lw}{2})

Each interior angle of a regular polygon is 120 degrees greater than each exterior angle. How many sides are there in the polygon?

A stairway 10ft high is such that each step accounts for half a foot upward and one-foot forward. What distance will an ant travel if it starts from ground level to reach the top of the stairway?

- 30 ft
- 33 ft
- 10 ft
- 29 ft

Find the area of the sector covered by the hour hand after it has moved through 3 hours if the length of the hour hand is 7cm.

- 77 sq.cm
- 38.5 sq.cm
- 35 sq.cm
- 70 sq.cm

Find the number of triangles in an octagon.

- 326
- 120
- 56
- Cannot be determined

What is the circum radius of a triangle whose sides are 7, 24 and 25 respectively?

What is the measure of in radius of the triangle whose sides are 24, 7 and 25?

- 12.5
- 3
- 6
- None of these

If ABC is a right angle triangle with angle A = 900 and 2s = a + b + c, where a > b > c where notations have their usual meanings, then which one of the following is correct?

- (s – b) (s – c) > s (s – a)
- (s – a) (s – c) > s (s – b)
- (s – a) (s – b) < s (s – c)
- 4s (s – a) (s – b) (s – c) = bc

If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?

- 10 sides
- 8 sides
- 12 sides
- 9 sides

What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41?

In the diagram below, CD = BF = 10 units and ∠CED = ∠BAF = 30

^{o}. What would be the area of triangle AED? (Note: Diagram below may not be drawn to scale.)

- 100 x (\\sqrt2) + 3)
- \\frac {100} {\left ( {{\sqrt {3+4}}} \right )})
- \\frac {50} {\left ( {{\sqrt {3+4}}} \right )})
- 50 x (\\sqrt3) + 4)

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## XAT TANCET Practice Questions - Listed Topic wise

- Number Theory
- Permutation Combination
- Probability
- Inequalities
- Geometry
- Coordinate Geometry
- Mensuration
- Trigonometry
- Data Sufficiency
- Percentages
- Profit Loss
- Ratio Proportion
- Mixtures & Alligation
- Speed Distance & Time
- Pipes, Cisterns & Work, Time
- Simple & Compound Interest
- Races
- Averages & Statistics
- Progressions : AP, GP & HP
- Set Theory
- Clocks Calendars
- Linear & Quadratic Equations
- Functions
- English Grammar
- General Awareness