Geometric proof using small angles

A question is this type if and only if it involves a geometric diagram (typically a circle) and requires proving a relationship involving small angle θ using geometric reasoning and small angle approximations.

1 questions · Challenging +1.2

Sort by: Default | Easiest first | Hardest first

OCR MEI Paper 3 2018 June Q3

2 marks Challenging +1.2

3 Fig. 3 shows a circle with centre O and radius 1 unit. Points A and B lie on the circle with angle \(\mathrm { AOB } = \theta\) radians. C lies on AO , and BC is perpendicular to AO . \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{31bc8bde-8d37-4e97-94e2-e3e73aab55e9-4_648_627_1507_717} \captionsetup{labelformat=empty} \caption{Fig. 3}

\end{figure} Show that, when \(\theta\) is small, \(\mathrm { AC } \approx \frac { 1 } { 2 } \theta ^ { 2 }\).