logo

Ask Questions, Get Answers

X
 

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y) passing through origin and touching the circle C externally, then the radius of T is equal to

$\begin{array}{1 1}(A)\;\large\frac{\sqrt 3}{\sqrt 2}\\(B)\;\large\frac{\sqrt 3}{2}\\(C)\;\large\frac{1}{2}\\(D)\;\large\frac{1}{4}\end{array} $

1 Answer

$CT^2 = (1-0)^2 + (1-y)^2$
also $CT = 1 + y$
$\therefore (1+y)^2 = 1 + (1-y)^2$
$1^2 + 2y + y^2 = 1 +1^2 - 2y + y^2$
$2y +2y = 1 + 1^2 +y^2-1^2- y^2$
$4y = 1$
$\implies y = \frac{1}{4}$
Hence the radius of T is $\frac{1}{4}$
answered Apr 7, 2014 by sreemathi.v
edited Nov 6 by priyanka.c
 

Related questions

...