by Naveen Neredimalli Sat 30 Mar 2024 11:47 PM 1000

Geometry Circles questions are crucial concepts in the Geometry section of the CAT Quantitative Aptitude. While these questions may not be overly challenging, it's essential to have a solid grasp of all theĀ Important Formulas in CAT Circles. Practice solving various CAT Geometry Circles questions from previous year papers to enhance your problem-solving skills.Ā You can check out these CAT Geometry questions from the CAT Previous year papers.

Keep practising free CAT mocks where you'll get a fair idea of how questions are asked, and type of questions asked of CAT Geometry Questions. These mock tests provide valuable insights into the question patterns and help you refine your strategies for tackling Geometry Circles questions effectively.

Also Read, CAT Eligibility Criteria 2024

Below are some key concepts and sample questions to aid your CAT 2024 preparation:

1. Basic Concepts:
• Circle Properties: Radius, Diameter, Circumference, Area.
• Tangents and Secants: Tangent lines, Secant lines, Tangent-secant theorem.
• Chords and Arcs: Arc length, Inscribed angles, Central angles.
• Special Circles: Circumcircle, Incircle.

1.Ā Tangents on a circleĀ

Tangents:

Direct common tangent: $$PQ^2=RS^2=D^2-\left(r_1-r_2\right)^2$$, where D is the distance between the centres:

Transverse common tangent: $$PQ^2=RS^2=D^2-\left(r_1+r_2\right)^2$$, where D is the distance between the centres:

#### Question 1

In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through Band C. Then the area, in sq. cm, of the overlapping region between the two circles is

#### Question 2

Let C1 and C2 be concentric circles such that the diameter of C1 is 2cm longer than that of C2. If a chord of C1 has length 6cm and is a tangent to C2, then the diameter, in cm, of C1 is

#### Question 3

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is

#### Question 4

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

#### Question 5

Two circles P and Q, each of radius 2 cm, pass through each otherās centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

#### Question 6

A circle of diameter 8 inches isĀ inscribed in a triangle ABC where $$\angle ABC = 90^\circ$$. If BC = 10 inches then the area of the triangle in square inches is

#### Question 7

Let C be the circle $$x^{2} + y^{2} + 4x - 6y - 3 = 0$$ and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to $$60^{\circ}$$. Then, the point at which L touches the line $$x$$ = 6 is

#### Question 8

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatĀ passes through points A and B where A is located 4 meters north of O and B is locatedĀ 3 meters east of O. Then, the length of PQ, in meters, is nearest to

#### Question 9

In the figure given below, the circle has a chord AB of length 12 cm, which makes an angle of $$60^\circ$$ at the center of the circle, O. ABCD, as shown in the diagram, is a rectangle. OQ is the perpendicular bisector of AB, intersecting the chord AB at P, the arc AB at M and CD at Q. OM = MQ. The area of the region enclosed by the line segments AQ and QB,and the arc BMA, is closest to (in cm$$^2$$):

#### Question 10

Mohanlal, a prosperous farmer, has a square land of side 2 km. For the current season, he decides to have some fun. He marks two distinct points on one of the diagonals of the land. Using these points as centers, he constructs two circles. Each of these circles falls completely within the land, and touches at least two sides of the land. To his surprise, the radii of both the circles are exactly equal to $$\frac{2}{3}$$ km. Mohanlal plants potatoes on the overlapping portion of these circles. Calculate the area on which Mohanlal planted potatoes (in sq. km).

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