Question

If one of the diameters of the circle x² + y² - 2x - 6y + 6 = 0 is a chord to the circle with centre (2, 1), then the radius of the circle is

(a)  √3

(b)  √2

(c)  3

(d)  √2

Answer 1

Correct option  (C) 3 

Explanation :

Let AB be a diameter of the circle x² + y² - 2x + 6y - 6 = 0 (see Fig). Centre of this circle is M = (1, 3) and radius √1² + 3² - 6 = 2 C(1, 2) is the centre of the required circle. Therefore

(CA)² = (AM)² + (CM)²

⁼ 4 + (2 -1)² + (3 -1)²

= 4 + 1 + 4 = 9

This implies CA = 3