Question

Chord of contact from any point on the line x + y = 4r to the circle $x^2+y^2=r^2$ (such that $r>0$) passes through the point (1, 1).What will be the value of r.

• A. 3
• B. 4
• C. 5
• D. 8

Answer 1

The correct option is B

4

Lets draw the diagram of the given circle, line and chord of contact.

Its given that any chord of contact of a point from P to the circle passes through (1, 1). The general point P can be of the form P ≡[k, 4r - k] . Chord of contact of P with respect to the circle is given by,

$T_1=0$

i.e., $kx+[4r-k]y=r^2$ ...........(1)

The chord of contact (1) passes through (1, 1),

i.e., k+4r-k=$r^2$

i.e., $r^2-4r=0$

r(r - 4) = 0

$\therefore$ r = 0 or 4

since radius $>$0

r = 4