<p>An isosceles triangle $PQR$, where $PQ=PR$, is inscribed in a circle with centre $O$ and radius $1$ unit. It is given that the angle $QOR=4\theta $ radians, where $\theta $ is an acute angle.</p>
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<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that $A$, the area of triangle $PQR$, can be expressed as $\left( \sin 2\theta \right)\left( 1+\cos 2\theta \right)$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Hence use differentiation to prove that $\theta $ varies, $A$ is a maximum when triangle $PQR$ is an equilateral triangle.</span></div><p style="text-align: right;">[5]</p></li></ol>

An isosceles triangle $PQR$, where $PQ=PR$, is inscribed in a circle with centre $O$ and radius $1$ unit. It is given that the angle $QOR=4\theta $ radians, where $\theta $ is an acute angle.

Show that $A$, the area of triangle $PQR$, can be expressed as $\left( \sin 2\theta \right)\left( 1+\cos 2\theta \right)$.

Hence use differentiation to prove that $\theta $ varies, $A$ is a maximum when triangle $PQR$ is an equilateral triangle.

2022 ACJC J2 MYE Q3

2022 ACJC J2 MYE Q3

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