Question

Find the radius of the smallest circle which touches the straight line 3x– y = 6 at (1, –3) and also touches the line y = x. complete up to one place of decimal.

Solution

Correct option is

r = 1.5

The two lines meet at B (3, 3) 

                                                               

 
   

 

      

    

        

                         

 Also from the figure,  

                

     

             

           

  

                       

                       

                          

                          

                        = 1.49 

                      r = 1.5. 

SIMILAR QUESTIONS

Q1

A square is formed by following two pairs of straight lines y2 – 14y + 45 = 0 and x2 – 8x + 12 = 0. A circle is inscribed in it. The centre of the circle is 

Q2

Let PQ and RS be tangents at the extremities the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals 

Q3

A diameter of x2 + y2 – 2x – 6y + 6 = 0 is a chord to circle (2, 1), then radius of the circle is 

Q4

If α, β, γ, δ be four angles of a cyclic quadrilateral taken in clockwise direction then the value of  will be:

Q5

A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

Q6

A circle passes through the point (–1, 7) and touches the line y = x at (1, 1). Its diameter is

Q7

Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Q8

Let a circle be given by 2x(x – a) + y(2y – b) = 0, (a  0, b ≠ 0). Find the condition on a and b, if two chords each bisected by the x – axis can be drawn to the circle from 

Q9

The equation of the locus of the mid points of the chords of the circle 4x2 + 4y2 – 12x + 4y + 1 = 0 that subtend an angle of  at its centre is:

Q10

Let S  x2 + y2 + 2gx + 2fy + c = 0 be a given circle. find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.