Test: Circles - 5 - Commerce MCQ

If a circle of constant radius 3k passes through the origin `O' and meets co-ordinate axes at A and B then the locus of the centroid of the triangle OAB is

A pair of tangents are drawn from the origin to the circle x² + y² + 20(x + y) + 20 = 0. The equation of the pair of tangents is

The locus of the centre of a circle which touches externally the circle, x² + y² – 6x – 6y + 14 = 0 and also touches the y-axis is given by the equation

The common chord of two intersecting circles C₁ and C₂ can be seen from their centres at the angles of 90º and 60º respectively. If the distance between their centres is equal to √3 + 1 then the radius of C₁ and C₂ are

A circle touches a straight line lx + my + n = 0 and cuts the circle x² + y² = 9 orthogonally, The locus of centres of such circles is

The length of the common chord of circles x² + y² – 6x – 16 = 0 and x² + y² – 8y – 9 = 0 is

If the two circles, x² + y² + 2g₁x + 2f₁y = 0 and x² + y² + 2g₂x + 2f₂y = 0 touches each other, then

If , ,  &  are four distinct points on a circle of radius 4 units then, abcd =

What is the length of shortest path by which one can go from (–2, 0) to (2, 0) without entering the interior of circle, x² + y² = 1

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circle internally is

In a right triangle ABC, right angled at A, on the leg AC as diameter, a semicircle is described. The chord joining A with the point of intersection D of the hypotenuse and the semicircle, then the length AC equals to

The circle passing through the distinct points (1, t), (t, 1) & (t, t) for all values of `t'. passes through the point

The locus of the mid points of the chords of the circle x² + y² – ax – by = 0 which subtend a right angle at  is

A circle is inscribed into a rhombus ABCD with one angle 60º. The distance from the centre of the circle to the nearest vertex is equal to 1. If P is any point of the circle, then | PA |² + | PB |² + | PC |² + | PD |² is equal to

Number of points (x, y) having integral coordinates satisfying the condition x² + y² < 25 is

Circles are drawn touching the co-ordinate axis and having radius 2, then

For the circles S₁ º x² + y² – 4x – 6y – 12 = 0 and S₂ º x² + y² + 6x + 4y – 12 = 0 and the line L º x + y = 0

x² + y² + 6x = 0 and x² + y² - 2x = 0 are two circles, then

3 circle of radii 1, 2 and 3 and centres at A, B and C respectively, touch each other. Another circle whose centre is P touches all these 3 circles externally. and has radius r. Also ∠PAB = q & ∠PAC = a.

Slope of tangent to the circle (x – r)² + y² = r² at the point (x, y) lying on the circle is

The centre(s) of the circle(s) passing through the points (0, 0), (1, 0) and touching the circle x² + y² = 9 is/are

Point M moved along the circle (x – 4)² + (y – 8)² = 20. Then it broke away from it and moving along a tangent to the circle cuts the x-axis at the point (–2, 0). The co-ordinates of the point on the circle at which the moving point broke away can be