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JEE Circle PYQs with Solutions

30 previous year questions from Circle (JEE Main & Advanced IOQM) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

30 questionsIOQMAnswers + solutions

About Circle PYQs

Circle has 30 previous year questions in the Quantrex Academy JEE Main & Advanced IOQM bank. The 30 questions in this list come from Olympiad workbook (30). Each question opens on its own page with the options, the correct answer and the worked solution where available.

Circle questions with solutions

1

Let A B C D be a convex cyclic quadrilateral. Suppose P is a point in the plane of the quadrilateral such that the sum of its distances from the vertices of ABCD is the least. If

Olympiad workbook Solution View → 2

Let Ω_1 be a circle with centre O and let AB be diameter of Ω_1 . Let P be a point on the segment OB different from O . Suppose another circle Ω_2 with centre P lies in the

Olympiad workbook Solution View → 3

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn through B . The distance of t from A is 25 and that from C is 16 . If S denotes the area of the

Olympiad workbook Solution View → 4

A light source at the point (0,16) in the coordinate plane casts light in all directions. A disc (a circle along with its interior) of radius 2 with center at (6,10) casts a

Olympiad workbook Solution View → 5

Let A B be a diameter of a circle ω and let C be a point on ω , different from A and B . The perpendicular from C intersects A B at D and ω at E(≠ C) . The circle with centre at C

Olympiad workbook Solution View → 6

Consider an isosceles triangle A B C with sides B C=30, C A=A B=20 . Let D be the foot of the perpendicular from A to B C , and let M be the midpoint of A D . Let P Q be a chord

Olympiad workbook Solution View → 7

A semicircular paper is folded along a chord such that the folded circular arc is tangent to the diameter of the semicircle. The radius of the semicircle is 4 units and the point

Olympiad workbook Solution View → 8

Let A B be a diameter of a circle and let C be a point on the segment A B such that A C: C B=6: 7 . Let D be a point on the circle such that D C is perpendicular to A B . Let D E

Olympiad workbook Solution View → 9

Let A B C be a triangle such that A B=A C . Suppose the tangent to the circumcircle of A B C at B is perpendicular of AC . Find ∠ ABC measured in degrees.

Olympiad workbook Solution View → 10

Let A B C D be a trapezium in which A B \| C D and A D ⊥ A B . Suppose A B C D has an incircle which touches AB at Q and CD at P . Given that PC=36 and QB=49 , Find PQ.

Olympiad workbook Solution View → 11

A village has a circular wall around it, and the wall has four gates pointing north, south east and west. A tree stands outside the village, 16 m north of the north gate, and it

Olympiad workbook Solution View → 12

Given a pair of concentric circles, chords A B, B C , C D, … of the outer circle are drawn such that they all touch the inner circle. If ∠ A B C=75^ ∘ , how many chords can be

Olympiad workbook Solution View → 13

Let A B and C D be two parallel chords in a circle with radius 5 such that the centre O lies between these chords. Suppose AB=6, CD=8 . Suppose further that the area of the part

Olympiad workbook Solution View → 14

Let A B C D be a square with side length 100 . A circle with center C and radius C D is drawn. Another circle of radius r , lying inside A B C D , is drawn to touch this circle

Olympiad workbook Solution View → 15

Two circles, S_1 and S_2 , of radii 6 units and 3 units respectively, are tangent to each other externally. Let A C and B D be their direct common tangents with A and B on S_1

Olympiad workbook Solution View → 16

Given a pair of concentric circles, chords A B, B C , C D, … of the outer circle are drawn such that they all touch the inner circle. If ∠ A B C=75^ ∘ , how many chords can be

Olympiad workbook Solution View → 17

A semicircular paper is folded along a chord such that the folded circular arc is tangent to the diameter of the semicircle. The radius of the semicircle is 4 units and the point

Olympiad workbook Solution View → 18

A light source at the point (0,16) in the coordinate plane casts light in all directions. A disc (a circle along with its interior) of radius 2 with center at (6,10) casts a

Olympiad workbook Solution View → 19

Let A B be a diameter of a circle ω and let C be a point on ω , different from A and B . The perpendicular from C intersects A B at D and ω at E(≠ C) . The circle with centre at C

Olympiad workbook Solution View → 20

Let A B C D be a square with side length 100 . A circle with center C and radius C D is drawn. Another circle of radius r , lying inside A B C D , is drawn to touch this circle

Olympiad workbook Solution View → 21

Consider an isosceles triangle A B C with sides B C=30, C A=A B=20 . Let D be the foot of the perpendicular from A to B C , and let M be the midpoint of A D . Let P Q be a chord

Olympiad workbook Solution View → 22

Two circles, S_1 and S_2 , of radii 6 units and 3 units respectively, are tangent to each other externally. Let A C and B D be their direct common tangents with A and B on S_1

Olympiad workbook Solution View → 23

Let A B C D be a convex cyclic quadrilateral. Suppose P is a point in the plane of the quadrilateral such that the sum of its distances from the vertices of ABCD is the least. If

Olympiad workbook Solution View → 24

Let A B be a diameter of a circle and let C be a point on the segment A B such that A C: C B=6: 7 . Let D be a point on the circle such that D C is perpendicular to A B . Let D E

Olympiad workbook Solution View → 25

Let Ω_1 be a circle with centre O and let AB be diameter of Ω_1 . Let P be a point on the segment OB different from O . Suppose another circle Ω_2 with centre P lies in the

Olympiad workbook Solution View → 26

Let A B and C D be two parallel chords in a circle with radius 5 such that the centre O lies between these chords. Suppose AB=6, CD=8 . Suppose further that the area of the part

Olympiad workbook Solution View → 27

A village has a circular wall around it, and the wall has four gates pointing north, south east and west. A tree stands outside the village, 16 m north of the north gate, and it

Olympiad workbook Solution View → 28

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn through B . The distance of t from A is 25 and that from C is 16 . If S denotes the area of the

Olympiad workbook Solution View → 29

Let A B C D be a trapezium in which A B \| C D and A D ⊥ A B . Suppose A B C D has an incircle which touches AB at Q and CD at P . Given that PC=36 and QB=49 , Find PQ.

Olympiad workbook Solution View → 30

Let A B C be a triangle such that A B=A C . Suppose the tangent to the circumcircle of A B C at B is perpendicular of AC . Find ∠ ABC measured in degrees.

Olympiad workbook Solution View →
Practice all Circle questions in the app →

Main Circle list

The larger JEE Circle list is under Mathematics (506 questions).

Related JEE IOQM chapters

Permutation and Combination (112)Basics of Mathematics (88)Properties of Triangles (64)Sequences and Series (38)Quadratic Equation (38)Straight Lines (24)Functions (20)Binary Numbers (8)Vector Algebra (6)Binomial Theorem (6)

Circle in other exams

BITSAT Circle (27)