Mathematics 0580 · IGCSE · Circle theorems II

Circle theorems II — practice question

Diagram (a): On the upper horizontal line, the points are A and C; on the lower horizontal line, the points are F, B and D; E is positioned beneath B. The angle at A is $26^{\circ}$. Triangle ABC is isosceles. AC is parallel to FBD. CBE is a straight line. The angle at B on the right-hand side is labelled $x^{\circ}$. Not drawn to scale. Diagram (b): A circle has diameter $PQ$, with P at the top and Q at the bottom. The tangent $SPT$ touches the circle at P. The angles shown inside are $17^{\circ}$ and $58^{\circ}$. The angle at the interior point is labelled $y^{\circ}$. Not drawn to scale.
(a)[3]

Determine the value of $x$.

(b)[5]

Determine the value of $y$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Application of isosceles-triangle or exterior-angle reasoning

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