Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

The sketch shows a circle with centre O and points B, D and E on the circumference. AOEF lies on one straight line. The straight line AC is tangent to the circle at B. The angle marked at A is $28^\circ$.
(a(i)(a))[1]

Write down the geometric name for line BOD.

(a(i)(b))[1]

Write down the geometric name for line ABC.

(a(ii))[2]

Write down the two geometric reasons that make angle AOB equal to $62^\circ$.

(a(iii))[1]

Give the geometric reason that angle DOE is also $62^\circ$.

(a(iv)(a))[1]

Calculate angle DEB.

(a(iv)(b))[2]

Calculate angle ODE.

(a(iv)(c))[2]

Calculate angle BEF.

(b)[2]

Write down two geometric properties that show a polygon is regular.

(c)[2]

Calculate the interior angle of a regular 10-sided polygon.

Worked solution & mark scheme

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