Question

In the circle given below, let $OA =1$ unit, $OB =13$ unit and $PQ \perp OB$. Then, the area of the triangle $PQB$ (in square units) is

• A. $24 \sqrt{2}$
• B. $24 \sqrt{3}$
• C. $26 \sqrt{3}$
• D. $26 \sqrt{2}$

Answer 1

Answer: (B)

$PA = AQ =\lambda$
$OA \cdot AB$
$= AP \cdot AQ$
$\Rightarrow 1.12=\lambda . \lambda$
$\Rightarrow \lambda=2 \sqrt{3}$
Area $\Delta PQB =\frac{1}{2} \times 2 \lambda \times AB$
$\Delta=\frac{1}{2} \cdot 4 \sqrt{3} \times 12$
$=24 \sqrt{3}$