Question

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Solution

Correct option is

b2 = ac

 

Let P (a cos θ, a sin θ) be a point on the circle x2 + y2 = a2.

Then equation of chord of contact of tangents drawn from  to the circle x2 + y2 = b2 is  

                   

    

∴ Length of perpendicular from (0, 0) to (1) = radius of (2)

  

SIMILAR QUESTIONS

Q1

 

Find the equation of the normal to the circle

x2 + y2 – 5x + 2y – 48 = 0 at the point (5, 6).

Q2

Find the equation of the tangents to the circle x2 + y2 = 16 drawn from the point (1, 4).

Q3

The angle between a pair of tangents from a point P to the circle x2 + y2+ 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. Find the equation of the locus of the point P.

Q4

Find the length of the tangents drawn from the point (3, – 4) to the circle 2x2 + 2y2 – 7x – 9y – 13 = 0.

Q5

Find the area of the triangle formed by tangents from the point (4, 3) to the circle x2 + y2 = 9 and the line segment joining their points of contact is 

Q6

Find the length of the tangent from any point on the circle x2 + y2 + 2gx+ 2fy + c = 0 to the circle x2 + y2 + 2gx + 2fy + c1 = 0 is

Q7

 

Find the power of point (2, 4) with respect to the circle 

                x2 + y2 – 6x + 4y – 8 = 0

Q8

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a straight line.

Q9

 

Find the condition that chord of contact of any external point

(hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle.

Q10

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).