In the diagram, $AB$ is a diameter of the circle with centre $O$. $DE$ and $BF$ are tangents

Question

In the diagram, $AB$ is a diameter of the circle with centre $O$. $DE$ and $BF$ are tangents to the circle at $C$ and $B$ respectively. $DCE$ and $BEF$ are straight lines. Prove that $\Delta ABC$ and $\Delta BFC$ are similar,[3] hence or otherwise, show that $\Delta CFE$ is an isosceles triangle.[4]

Accepted Answer

$(a)\ \triangle ABC\sim\triangle BFC$ (proven) $(b)\ CE=EF$, so $\triangle CEF$ is isosceles (shown)

2025 AHS PRELIMS P1 Q13

2025 AHS PRELIMS P1 Q13

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