Mathematics 4024 · O Level · Circle theorems I

Circle theorems I — practice question

Points A, B, C, D and E lie on the circumference of the circle with centre $O$. $AC$ is a diameter, and $AC$ is parallel to $ED$. The lines $AC$ and $BE$ intersect at $F$. $\angle BAC$ is $52^\circ$ and $\angle CBE$ is $68^\circ$.
(a(i))[1]

Find the size of $\angle ACB$.

(a(ii))[1]

Find $\angle AEF$. Explain your reasoning.

(a(iii))[1]

Find the size of $\angle CDE$.

(a(iv))[2]

Find the size of $\angle BCD$.

(b)[3]

Work out the measure of the largest angle in the pentagon shown.

(c)[2]

The quadrilateral angles are stated correct to the nearest degree. Find the lower bound for $y$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Therefore $\angle ACB = 38^\circ$

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