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Circle — JEE Main & Advanced IOQM PYQs

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

30 questionsIOQMSolutions on every page
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 P

Olympiad workbook Solution View → 2

Let ₁ be a circle with centre O and let AB be diameter of ₁ . Let P be a point on the segment OB different from O . Suppose another circle ₂ with centre P lies in the interior of ₁

Olympiad workbook Solution View → 3

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to 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 tr

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 shadow

Olympiad workbook Solution View → 5

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

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 of

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 o

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 b

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 ca

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 drawn befo

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 ext

Olympiad workbook Solution View → 15

Two circles, S₁ and S₂ , 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 S₁ , and C

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 drawn befo

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 o

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 shadow

Olympiad workbook Solution View → 19

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

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 ext

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 of

Olympiad workbook Solution View → 22

Two circles, S₁ and S₂ , 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 S₁ , and C

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 P

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 b

Olympiad workbook Solution View → 25

Let ₁ be a circle with centre O and let AB be diameter of ₁ . Let P be a point on the segment OB different from O . Suppose another circle ₂ with centre P lies in the interior of ₁

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 ca

Olympiad workbook Solution View → 28

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to 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 tr

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 →
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