10. (a) Show that the points A(-7, -2), B(2, 1) and C(17, 6) are collinear - Scottish Highers Maths - Question 10 - 2017

Given that the radius of circle D is the sum of the radii of circles A and B:

1. Find the respective radii:

   $r_a = \sqrt{10} \ \text{and} \ r_b = 2r_a = 2\sqrt{10}$

2. Calculate the radius of circle C:

   $r_c = r_a + r_b = \sqrt{10} + 2\sqrt{10} = 3\sqrt{10}$

3. The centre of circle D can be found as the midpoint of the line segment connecting the centres A and C:

   $\text{Centre D} = \left( \frac{-7 + 17}{2}, \frac{-2 + 6}{2} \right) = (5, 2)$

4. The equation of the circle with centre D and radius r_c is:

   $(x - 5)^2 + (y - 2)^2 = (3\sqrt{10})^2$

   $(x - 5)^2 + (y - 2)^2 = 90$