Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

The diagram depicts a circle with centre $O$ and diameter $AD$. Point $B$ lies on the circumference, and the straight line $CDE$ touches the circle at $D$. Also, $AD = 21$ cm and $CD = 16$ cm.
(a(i))[2]

Calculate the circumference of this circle.

(a(ii))[2]

Calculate the area of this circle.

(b(i))[1]

Write down the size of angle $ABD$.

(b(ii))[3]

Show that $AB = 19.0$ cm, to 3 significant figures.

(c(i))[2]

Calculate the area of triangle $ABD$.

(c(ii))[2]

Work out the combined area of the circle's shaded segments.

(d(i))[1]

Write down the mathematical name for line $CDE$.

(d(ii))[1]

Write down the mathematical name of line $OD$.

(d(iii))[2]

Use trigonometry to find the size of angle $OCD$.

Worked solution & mark scheme

This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: $66.0$, or any value from $65.97$ to $65.98\ldots$

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