Higher November 2018 Paper 1 Q26
26. In this question all dimensions are in centimetres.
The diagram shows a sketch of two circles, both with centre O.
Diagram not drawn to scale
The equation of the inner circle is \(x^2 + y^2 = 4\).
The equation of the outer circle is \(x^2 + y^2 = 144\).
The points \(A\) and \(B\) lie on the inner circle and outer circle respectively.
\(OAB\) is a straight line.
(a) Find the length of the line \(AB\).
You must show all your working. [2]
You must show all your working. [2]
(b) Write down the equation of the tangent to the outer circle at the point \(B\). [1]
| Scheme | Marks | Comments |
|---|---|---|
| \(\sqrt{144} - \sqrt{4} = 10\) or \(12 - 2 = 10\) | B2 | B1 for \(\sqrt{144} - \sqrt{4}\) or for (radius of outer circle =) 12 or (radius of inner circle =) 2 seen |
| Scheme | Marks | Comments |
|---|---|---|
| \(y = -12\) | B1 | |
| (3) |