Mathematics 0580 · IGCSE · Circle theorems II

Circle theorems II — practice question

In the diagram, $EH$ runs parallel to $FG$. The lines $EG$ and $FH$ cross at $Z$. Angle $ZFG = 27^\circ$.
(a(i))[1]

Find $x$.

(a(ii))[2]

Calculate the length of $EZ$.

(b)[3]

Find angle $ADC$.

(c(i))[2]

Complete this statement: Angle $QPS$ = angle $QRS$ = ............ $^\circ$ because ................................................

(c(ii))[2]

Complete this statement: Angle $SQP$ = ............ $^\circ$ because ................................................

(c(iii))[1]

The results of part (c)(i) and part (c)(ii) show that the cyclic quadrilateral $PQRS$ is a ................................................

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