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Q.) The chord of contact of tangents from three points A, B, C to the circle x² + y² = a² are concurrent, then A, B, C will
[A]
be concyclic
[B]
be collinear
[C]
form the vertices of a triangle
[D]
None of these
[A] be concyclic
[B] be collinear
[C] form the vertices of a triangle
[D] None of these
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Circles 📚
1
If the equation of any two diagonals of a regular pentagon belongs to family of lines (1+2a)y-(2+a)x ...
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
The line 2x-y+1 =0 is tangent to the circle at the point (2, 5) and the centre of the circles lies o ...
5
In a triangle ABC, right angled at A, on the leg AC as diameter, a semicircle is described. If a cho ...
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
Two congruent circles with centres at (2, 3) and (5, 6), which intersect at right angles, have radiu ...
9
A circle of radius unity is centred at origin. Two particles start moving at the same time from the ...
10
The value of 'c' for which the set {(x, y) | x² + y² + 2x ≤ 1} ∩ {(x,y) | x - y + c) >= 0} contains ...
11
A circle is inscribed into a rhombus ABCD with one angle 60°. The distance from the centre of the ci ...
12
B and C are fixed points having coordinates (3, 0) and (-3, 0), respectively. If the vertical angle ...
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
A line meets the co-ordinate axes in A and B. A circle is circumscribed about the triangle OAB. If d ...
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
Tangents are drawn to the circle x² + y² = 1 at the points where it is met by the circle x² +y^2- ( ...
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
If the line x cos θ + y sin θ = 2 is the equation of a transverse common tangent to the circles x² ...
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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