Edexcel IGCSE Math A 4.6.HA intersecting chord properties

Practise intersecting-chord questions by multiplying the two parts of each chord, forming an equation and solving for the unknown.

Exam points

Form an equation from products of intersecting chord segments inside a circle.
Solve for unknown lengths such as x or y after applying the chord product rule.
Use the circle diagram to connect chord lengths with angle information when required.

[Maximum number: 2]

Diagram NOT accurately drawn

PTR and QTS are chords of a circle.
$P T=(3 y-5) \mathrm{cm} \quad Q T=(y+3) \mathrm{cm} \quad R T=4 x \mathrm{~cm} \quad S T=(x+2) \mathrm{cm}$
Find an expression for y in terms of x

By the intersecting chords theorem,

(y+3)(x+2)=4x(3y-5).

Expand:

xy+2y+3x+6=12xy-20x.

Collect terms in y:

20x+3x+6=12xy-xy-2y

23x+6=y(11x-2).

Final answer:

y=\frac{23x+6}{11x-2}.

M1 for forming a correct intersecting-chords equation. M1 for expanding. M1ft for collecting y-terms and non-y-terms. M1ft for factorising for y. A1 for the expression.

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4.6.HA Intersecting chord properties question 1