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Q.) Any circle through the point of intersection of the lines x + √3y = 1 and √3x = y + 2 intersects these lines at points P and Q. The angle subtended by the arc PQ at its centre is
[A]
180°
[B]
90°
[C]
120°
[D]
Depends on centre and radius
[A] 180°
[B] 90°
[C] 120°
[D] Depends on centre and radius
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Circles 📚
1
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2
If OA and OB are equal perpendicular chords of the circles x²+y²-2x+4y=0, then equations of OA and O ...
3
Equation of chord of the circle x²+ y²-3x-4y-4=0, which passes through the origin such that the orig ...
4
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5
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6
A rhombus is inscribed in the region common to the two circles x²+y²-4x-12=0 and x²+y²+4x-12=0 with ...
7
The locus of the point (2, 3) such that it is the midpoint of the chord 5x+2y=16 ...
8
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9
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10
The value of 'c' for which the set {(x, y) | x² + y² + 2x ≤ 1} ∩ {(x,y) | x - y + c) >= 0} contains ...
11
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12
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13
ABCD is a square of unit area. A circle is tangent to two sides of ABCD and passes through exactly o ...
14
A circle of radius unity is centred at origin. Two particles start moving at the same time from the ...
15
The value of 'e' for which the set {(x, y) | x² + y² + 2x ≤ 1} ∩ {(x,y) | (x - y + c²) > 0} contains ...
16
A circle is inscribed into a rhombus ABCD with one angle 60°. The distance from the centre of the ci ...
17
Two circles with radii a and b touch each other externally such that θ is the angle between the dire ...
18
A pair of tangents are drawn to a unit circle with center at the origin and these tangents intersect ...
19
A straight line with slope 2 and y-intercept 5 touches the circle, x² + y² + 16x + 12y + c = 0 at a ...
20
A circle of constant radius 'a' passes through origin O and cuts the axes of co-ordinates in points ...
21
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22
If a circle of constant radius 3k passes through the origin 'O' and meets co-ordinate axes at A and ...
23
The equation of a line inclined at an angle π/4 to the X-axis, such that the two circles x² + y² = 4 ...
24
Let C be a circle with two diameters intersecting at an angle of 30°. A circle S is tangent to both ...
25
A straight line, with equation x = 2y + 10 meets the circle with equation x² + y² = 100 at B in the ...
26
Let a and b represent the length of a right triangle's legs. If d is the diameter of a circle inscr ...
27
If the chord y=mx +1 of the circle x² + y² = 1 subtends an angle 45° at the major segment of the cir ...
28
A variable chord of circle x² + y² = 4 is drawn from the point P(3, 5) meeting the circle at the po ...
29
In triangle ABC, equation of side BC is x-y=0, Circumcentre and orthocentre of the triangle are (2, ...
30
The range of values of r for which the point (-5+r/2,-3+r/2) is an interior point of the major seg ...
31
A square is inscribed in the circle x²+y²-2x+4y-93=0 with its sides parallel to the coordinate axis. ...
32
(-6, 0), (0, 6) and (-7, 7) are the vertices of a triangle ABC. The incircle of the triangle has th ...
33
The angle at which the circles (x - 1)² + y² = 10 and x² + (y-2)² = 5 intersect is ...
34
A tangent at a point on the circle x² + y² = a² intersects a concentric circle at two points P and ...
35
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36
If point A is (1, 0) and point B is (0, 1). If point C is on the circle x² + y² = 1, then the locus ...
37
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38
Any circle through the point of intersection of the lines x + √3y = 1 and √3x = y + 2 intersects th ...
39
If the angle between tangents drawn to x² + y² + 2gx + 2fy + c = 0 from (0, 0) is π/2, then ...
40
The common chord of the circle x² + y² + 6x + 8y - 7=0 and a circle passing through the origin, and ...
41
The chord of contact of tangents from three points A, B, C to the circle x² + y² = a² are concurren ...
42
Radius of the tangent circle that can be drawn to pass through the point (0, 7), (0, 6) and touchin ...
43
The equation of the tangent to the circle x² + y² = a², which makes a triangle of area a² with the ...
44
If the circle x² + y² + 2gx + 2fy + c = 0 is touched by y = x at P such that OP = 6√2, then the val ...
45
The circle x² + y² = 4 cuts the line joining the points A(1, 0) and B(3, 4) in two points P and Q. ...
46
The area of the triangle formed by the positive x-axis and the normal and tangent to the circle x² ...
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