Mathematics 0580 · IGCSE · Circle theorems I

Circle theorems I — practice question

ABCDEF forms a regular hexagon, and $DF$, $DA$ and $DB$ are diagonals.
(a)[2]

Complete the statements below by using three different triangles. Triangle $DEF$ is congruent to triangle [BLANK]. Triangle [BLANK] is congruent to triangle [BLANK].

(b)[5]

Finish the statements and reasons. In triangles $OPT$ and $OQT$: $OP = [BLANK]$ because each one is a radius of the circle. $OT$ is the side shared by both triangles. Angle $OPT =$ angle $[BLANK] = 90^{\circ}$ because [BLANK]. Triangles $OPT$ and $OQT$ are congruent by the criterion [BLANK]. This shows that the tangents $TP$ and $TQ$ are [BLANK].

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: The congruent pairs are $[DEF,BCD]$ and $[ADF,ADB]$.

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