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
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 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