Higher June 2022 Paper 1 Q10
10 Two circles, \(C_1\) and \(C_2\), are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis.
The centre of circle \(C_1\) is at the point with coordinates (–1, 3) and the radius of \(C_1\) is 13 cm.
The centre of circle \(C_2\) is at the point with coordinates (7, 18) and the radius of \(C_2\) is 6 cm.
(a) Work out the distance between the centre of \(C_1\) and the centre of \(C_2\) (3)
(b) Explain why circle \(C_1\) intersects circle \(C_2\) (1)
| Scheme | Marks |
|---|---|
| \((18 - 3)^2 + (7 - -1)^2\) oe or \(15^2 + 8^2\) (= 289) oe | M1 |
| \(\sqrt{(18 - 3)^2 + (7 - -1)^2}\) \(\left(= \sqrt{\text{``}{289}\text{''}}\right)\) | M1 |
| 17 | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| 13 + 6 > “17” Answer: correct reason | A1ft |
| (1) | |
| (4 marks) |
Notes
A1ft: dep M1
Acceptable examples
“They overlap by 2cm”
“The distance between the centres is less than the sum of the radii”
“17 is less than the distance than the total of the radii”
“19 is bigger than the distance between the centres”
Not acceptable examples
“19 is greater than the distance between the circles” oe
“The circumference of each circle overlaps”