Comprehension Based Questions: Circle - Free MCQ Practice Test with solutions,
MCQ Practice Test & Solutions: Test: Comprehension Based Questions: Circle (8 Questions)
You can prepare effectively for JEE Crack JEE with 35 Years of Previous Year Solved Papers with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Comprehension Based Questions: Circle". These 8 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 10 minutes
- - Number of Questions: 8
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PASSAGE-1
ABCD is a square of side length 2 units. C1 is the circle touching all the sides of the square ABCD and C2 is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.
Q. If P is any point of C1 and Q is another point on C2, then
is equal to (2006 - 5M, –2)
ABCD is a square of side length 2 units. C1 is the circle touching all the sides of the square ABCD and C2 is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.
is equal to (2006 - 5M, –2) Detailed Solution: Question 1
,0 ).
PASSAGE-1
ABCD is a square of side length 2 units. C1 is the circle touching all the sides of the square ABCD and C2 is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.
Q. If a circle is such that it touches the line L and the circle C1 externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is (2006 - 5M, –2)
ABCD is a square of side length 2 units. C1 is the circle touching all the sides of the square ABCD and C2 is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.
Detailed Solution: Question 2
PASSAGE-1
ABCD is a square of side length 2 units. C1 is the circle touching all the sides of the square ABCD and C2 is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.
Q. A line L' through A is drawn parallel to BD. Point S moves such that its distances from the line BD and the vertex A are equal. If locus of S cuts L' at T2 and T3 and AC at T1, then area of ΔT1T2T3 is (2006 - 5M, –2)
ABCD is a square of side length 2 units. C1 is the circle touching all the sides of the square ABCD and C2 is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.
Detailed Solution: Question 3
is the vertex of parabola.
PASSAGE-2
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation
and the point D is
Further, it is given that the origin and the centre of C are on the same side of the line PQ.
Q. The equation of circle C is (2008)
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation
and the point D isDetailed Solution: Question 4
or 
should be the coordinates of C.
PASSAGE-2
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equationand the point D is
Further, it is given that the origin and the centre of C are on the same side of the line PQ.
Q. Points E and F are given by (2008)
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation
and the point D isDetailed Solution: Question 5
and 
PASSAGE-2
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equationand the point D is
Further, it is given that the origin and the centre of C are on the same side of the line PQ.
Q. Equations of the sides QR, RP are (2008)
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation
and the point D isDetailed Solution: Question 6
and equation of side RP is y = 0PASSAGE-3
A tangent PT is drawn to the circle x2 + y2 = 4 at the point 
. A straight line L, perpendicular to PT is a tangent to the circle (x – 3)2 + y2 = 1. (2012)
Q. A possible equation of L is
A tangent PT is drawn to the circle x2 + y2 = 4 at the point
. A straight line L, perpendicular to PT is a tangent to the circle (x – 3)2 + y2 = 1. (2012)Detailed Solution: Question 7
= – 1 or – 5
PASSAGE-3
A tangent PT is drawn to the circle x2 + y2 = 4 at the point . A straight line L, perpendicular to PT is a tangent to the circle (x – 3)2 + y2 = 1. (2012)
Q. A common tangent of the two circles is
A tangent PT is drawn to the circle x2 + y2 = 4 at the point
. A straight line L, perpendicular to PT is a tangent to the circle (x – 3)2 + y2 = 1. (2012)Detailed Solution: Question 8
36 m2 = 4(m2 + 1)
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