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
Let O be the centre of the circle of unit radius and the coordinates of A0 be (1, 0).
Since each side of the regular hexagon makes an angle of 60o at the centre O.
A3 are (–1, 0)
The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by
A circle touches both the coordinates axes and the line the coordinates of the centre of the circle can be
If the tangent at the point P on the circle x2 + y2 + 6x + 6y = 2 meets the straight line 5x – 2y + 6 = 0 at a point Q on the y-axis, then the length ofPQ is
If a > 2b > 0 then the positive value of m for which is a common tangent to x2 + y2 = b2 and (x – a)2+ y2 = b2 is
Let PQ and RS be tangents at the extremities of a diameter PR of a circle of radius r. Such that PS and RQ intersect at a point X on the circumference of the circle, then diameter of the circle equals.
A triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have coordinates (3, 4) and (–4, 3) respectively, then ∠QPR is equal to
For each natural number k, let Ck denote the circle with radius k centimeters and centre at the origin O, on the circle Ck a particle moves k centimeters in the counter-clockwise direction. After completing its motion on Ck, the particle moves to Ck + 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 Cn’ 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
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