Basics of Circles — CAT Previous-Year Questions
27 previous-year questions on Basics of Circles from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Basics of Circles · CAT PYQs
A circular plot of land is divided into two regions by a chord of length 10√3 meters such that the chord subtends an angle of 120° at the center. Then, the area, in square meters, of the smaller region is
All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is
Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to
The vertices of a triangle are (0, 0), (4, 0) and (3, 9). The area of the circle passing through these three points is
In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to
In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is
A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semicircle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm.) will be:
What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is
In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE : EB = 1 : 2, and DF is perpendicular to MN such that NL : LM = 1 : 2. The length of DH in cm is
P, Q, S, and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?
On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC?
Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid-point of the line segment P0B, P2 is the mid-point of the line segment P1B and so on. Let C1, C2, C3, ... be circles with diameters P0P1, P1P2, P2P3 ... respectively. Suppose the circles C1,C2, C3, ... are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is:
In the figure given below, AB is the chord of a circle with centre O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ∠ACD = y° and ∠AOD = x° such that x = ky, then the value of k is
In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?
In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with centre at O. The length of side AB is greater than that of side BC.
The ratio of the area of the circle to the area of the recrangle ABCD is π : .
The line segment DE intersects AB at E such that ∠ODC = ∠ADE. What is the ratio AE : AD?
A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, three km north of the north gate, and it can just be seen from a point nine km east of the south gate. What is the diameter of the wall that surrounds the city?
Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.
A square is inscribed in a circle. What is the difference between the area of the circle and that of the square?
- The diameter of the circle is 25 cm.
- The side of the square is 25 cm.
Consider a circle with unit radius. There are 7 adjacent sectors, S1, S2, S3,...., S7 in the circle such that their total area is (1/8)th of the area of the circle. Further, the area of the jth sector is twice that of the (j –1)th sector, for j = 2, ..., 7. What the angle, in radians, subtended by the arc of S1 at the centre of the circle?
Direction: Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as
1. if the question can be answered with the help of any one statement alone but not by the other statement.
2. if the question can be answered with the help of either of the statements taken individually.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.
A circle circumscribes a square. What is the area of the square?
I. Radius of the circle is given.
II. Length of the tangent from a point 5 cm away from the centre of the circle is given.
AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral ACBD.
In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of Δ CBE to that of Δ ADE?
The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of ΔABC.
In the given figure, AB is diameter of the circle and points C and D are on the circumference such that ∠CAD = 30° and ∠CBA = 70°. What is the measure of ∠ACD?
