Question

Let a circle C : (x – h)2 + (y – k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.

Answer 1

The correct answer is 7

Fig. Circle

Here, $OM^2 = OP^2 – PM^2$
$(|\frac{1+r}{\sqrt2}|)^2 = r^2-1$
$∴ r^2 – 2r – 3 = 0$
∴ r = 3
∴ Equation of circle is
$(x−1)^2+(y−3)^2=3^2$
∴ h = 1, k = 3, r = 3
∴ h + k + r = 7