SEAMO 2021 — Paper E — Grade 9–10 Question 7

Question 7

In $\triangle ABC$, $\angle A=30^\circ$, $\angle C=90^\circ$, $AC=1$. Construct equilateral triangles $BCP,CAQ,ABR$ externally. Let $T=QR\cap AB$. Find $[PQT]$.

Question illustration

$\frac{4\sqrt2}{3}$
$\frac12$
$\frac{3\sqrt3}{8}$
$\frac{\sqrt5}{2}$
None of the above