Circle Theorems: Eduqas GCSE Higher June 2017 Paper 1 Q17

Higher June 2017 Paper 1 Q17

EduqasHigherCurrent spec4 marksCircle Theorems Pythagoras

17. In this question all dimensions are in centimetres.
The diagram shows a sketch of two circles, both with centre O.

Two circles centred at the origin O on x and y axes; the chord AB of the outer circle touches the inner circle at the bottom, on the y-axis

Diagram not drawn to scale

The line AB is a chord of the outer circle and a tangent to the inner circle.
The length of AB is 24.
The equation of the outer circle is \(x^2 + y^2 = 13^2\).

Find the equation of the inner circle. [4]

Mark scheme

Scheme	Marks	Comments
Radius of outer circle = 13 or half the chord = 12	B1	May be on diagram
(radius inner circle)\(^2 + 12^2 = 13^2\)	M1
\(r = 5\) seen or implied	A1
\(x^2 + y^2 = 5^2\)	A1	FT ‘their derived 5’ If zero scored allow SC1 for \(12^2 + 5^2 = 13^2\) or \(12^2 + 5^2 = 169\) only
	(4)