4400 Higher November 2008 Paper 3 Q20

EdexcelHigherOld spec5 marksCircle Theorems Pythagoras

Circle centre C with radius r cm; tangent AB = 3 cm touching the circle at B; ADC a straight line with AD = 2 cm

Diagram NOT accurately drawn

\(B\) and \(D\) are points on a circle, centre \(C\).
\(AB\) is the tangent to the circle at \(B\).
\(ADC\) is a straight line.
\(AB = 3\) cm.
\(AD = 2\) cm.

The radius of the circle is \(r\) cm.
Find the value of \(r\).

(5)

Mark scheme

Scheme	Marks
eg \(r^2 + 9 = (r + 2)^2\) \(r^2 + 3^2 = (r + 2)^2\) \(r = \sqrt{(r + 2)^2 - 9}\) \(r + 2 = \sqrt{r^2 + 9}\)	M2
\(r^2 + 9 = r^2 + 4r + 4\)	B1
\(4r = 5\)	M1
\(1\frac{1}{4}\) or 1.25	A1
	(5)
	(5 marks)

Notes

M2: for correct use of Pythagoras’ Rule
M1 for \(r^2 + 3^2\) or \(r^2 + 9\) or \((r + 2)^2\)

A1: Accept \(\frac{5}{4}\)