Two Circles Are Inscribed And Circumscribes About A Square ABCD, Length Of Each Side Of The Square Is 32. P and Q are Points Respectively Of These Circles, Then  is Equal To

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 

Angle of intersection of these circle is

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

A triangle has two of its sides along the axes, its third side touches the circle x² + y² – 2ax – 2ay + a² = 0. If he locus of the circumcentre of the triangle passes through the point (38, –37) then a² – 2a is equal to

Let A be the centre of the circle x² + y² – 2x – 4y – 20 = 0. The tangents at the point B(1, 7) and C(4, –2) on the circle meet at the point D. If Δ denotes the area of the quadrilateral ABCD, then 45Δ is equal to