Angle Of Intersection Of These Circle Is

For each natural number k, let C_k denote the circle with radius k centimeters and centre at the origin O, on the circle C_k a particle moves k centimeters in the counter-clockwise direction. After completing its motion on C_k, the particle moves to C_{k + 1} in the radial direction. The motion of the particle continues in this manner. The particle starts at (1, 0). If the particle crosses the positive direction of x-axis for the first time on the circle C_n’ then n =

If the area of the quadrilateral formed by the tangent from the origin to the circle x² + y² + 6x – 10y + c = 0 and the pair of radii at the points of contact of these tangents to the circle is 8 square units, then c is a root of the equation

If two distinct chords, drawn from the point (p, q) on the circle x² + y²= px + qy (where pq ≠ 0) are bisected by the x-axis, then

Let A₀ A₁ A₃ A₄ A₅ be a regular hexagon inscribed in a unit circle with centre at the origin. Then the product of the lengths of the line segmentsA₀ A₁, A₀ A₂ and A₀ A₄ is

C₁ and C₂ are circles of unit radius with centres at (0, 0) and (1, 0) respectively. C₃ is a circle of unit radius, passes through the centres of the circles C₁ and C₂ and have its centre above x-axis. Equation of the common tangent to C₁ and C₃ which does not pass through C₂ is

A chord of the circle x² + y² – 4x – 6y = 0 passing through the origin subtends an angle tan^-1 (7/4) at the point where the circle meets positivey-axis.

Equation of the chord is

On the line joining the points A (0, 4) and B (3, 0), a square ABCD is constructed on the side of the line away from the origin. Equation of the circle having centre at C and touching the axis of x is 

A circle with centre at the origin and radius equal to a meets the axis of x at A and B.P (α) and Q (β) are two points on this circle so that α – β = 2γ, where γ is a constant. The locus of the point of intersection of APand BQ is

A circle C₁ of radius b touches the circle x² + y² = a² externally and has its centre on the positive x-axis; another circle C₂ of radius c touches the circle C₁ externally and has its centre on the positive x-axis. Given a< b < c, then the three circles have a common tangent if a, b, c are in 

If C₁, C₂ are the centre of these circles than area of Δ OC₁ C₂, where Ois the origin, is