XAT Triangles, Circles & Quadrilaterals MCQs with Solutions: Practice XAT Previous Year Questions (PYQs)

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Triangles, Circles & Quadrilaterals is an important topic in the Quantitative Ability and Data Interpretation section in XAT exam. Practising this topic will increase your score overall and make your conceptual grip on XAT exam stronger.

This article gives you a full set of XAT Triangles, Circles & Quadrilaterals MCQs with explanations and XAT previous year questions (PYQs) for effective practice. Practice of Quantitative Ability and Data Interpretation MCQs including Triangles, Circles & Quadrilaterals questions regularly will improve accuracy, speed, and confidence in the XAT 2026 exam.

Also Check : XAT 2026 Question Paper with Solutions PDF

XAT Triangles, Circles & Quadrilaterals MCQs with Solutions

1.
The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.
In a cricket match, three slip fielders are positioned in a straight line. The distance between the 1st slip and the 2nd slip is the same as the distance between the 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and player X?
1. The ball travels at a speed of 3.6 km/hour.
2. The distance between the 1st slip and the 3rd slip is 2 meters.
- Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
- Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.
- Each statement alone is sufficient.
- Both statements together are sufficient, but neither of them alone is sufficient.
- Statements 1 & 2 together are not sufficient.
View Solution
2.
ABC is a triangle and the coordinates of A, B, and C are (a, b - 2c), (a, b + 4c), and (-2a, 3c), respectively, where a, b, and c are positive numbers. The area of the triangle ABC is:
- 6abc
- 9abc
- 6bc
- 9ac
- None of the above
View Solution
3.
ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB . Kindly note that BC<AD . P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC . If the area of the triangle CPD is 4√3. Find the area of the triangle ABQ.
- 2√3
- 4√3
- 4
- 8√3
- None of the above
View Solution
4.
A square is inscribed in an equilateral triangle such that one of the sides of the square completely lies on one of the sides of the equilateral triangle. Find the ratio of the perimeters of the square and equilateral triangle.
- \(\frac{4}{3+2\sqrt3}\)
- \(\frac{2\sqrt3}{3\sqrt 3+6}\)
- \(\frac{\sqrt3}{3\sqrt 3+6}\)
- \(\frac{5}{3+2\sqrt 3}\)
- None of these
View Solution
5.
ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB²-AE²+6CD is:
- 5
- 10
- 14
- 18
- 21
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XAT Triangles, Circles & Quadrilaterals MCQs with Solutions

2.ABC is a triangle and the coordinates of A, B, and C are (a, b - 2c), (a, b + 4c), and (-2a, 3c), respectively, where a, b, and c are positive numbers. The area of the triangle ABC is:

3.ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB . Kindly note that BC<AD . P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC . If the area of the triangle CPD is 4√3. Find the area of the triangle ABQ.

4.A square is inscribed in an equilateral triangle such that one of the sides of the square completely lies on one of the sides of the equilateral triangle. Find the ratio of the perimeters of the square and equilateral triangle.

5.ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB2-AE2+6CD is:

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2.
ABC is a triangle and the coordinates of A, B, and C are (a, b - 2c), (a, b + 4c), and (-2a, 3c), respectively, where a, b, and c are positive numbers. The area of the triangle ABC is:

3.
ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB . Kindly note that BC<AD . P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC . If the area of the triangle CPD is 4√3. Find the area of the triangle ABQ.

4.
A square is inscribed in an equilateral triangle such that one of the sides of the square completely lies on one of the sides of the equilateral triangle. Find the ratio of the perimeters of the square and equilateral triangle.

5.
ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB²-AE²+6CD is: