Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

The diagram shows that $ABC$ is a straight line. $AD$ runs parallel to $BE$, $ ngle BAD = 34^\circ$ and $AB = BD$. The angles at the marked points are labelled $p^\circ$, $q^\circ$, $r^\circ$, $t^\circ$ and $s^\circ$. A second diagram presents a circle with centre $O$, points $B$ and $D$ on the circumference, line $AC$ touching the circle only at $B$, and $BD$ as a straight line passing through $O$.
(a(i)(a))[2]

$p = \ldots$ since $\ldots$

(a(i)(b))[2]

$q = \ldots$ since $\ldots$

(a(ii))[2]

Calculate the value of $r$ and the value of $s$.

(a(iii))[2]

Find the value of $t$ and give a reason for your answer.

(b)[2]

Complete the statement. $\angle ABD = \ldots$ because $\ldots$

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: The angle is $34^\circ$

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