Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

A, B, C and D lie on the circle with centre O. EF is tangent to the circle at D. Angle ADE = 42^{\circ} and angle COD = 162^{\circ}.
(a(i))[2]

Find angle $x$, and justify your answer.

(a(ii))[2]

Find angle $y$, and give reasons for your answer.

(a(iii))[3]

Find angle $z$, and give reasons for your answer.

(b(i))[3]

Explain why triangle PQR is similar to triangle PUT. Provide a reason for each statement you make.

(b(ii)(a))[1]

Find the ratio of $PU$ to $PQ$.

(b(ii)(b))[3]

Find the area enclosed by quadrilateral QRTU.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: The angle is $81^{\circ}$.

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