In the circle given below,


In the circle given below, let $O A=1$ unit, $O B=13$ unit and $P Q \perp O B$.

Then, the area of the triangle PQB (in square units) is:


  1. (1) $26 \sqrt{3}$

  2. (2) $24 \sqrt{2}$

  3. (3) $24 \sqrt{3}$

  4. (4) $26 \sqrt{2}$

Correct Option: , 3






In $\Delta \mathrm{PAC}$


$P A=\sqrt{12}$

$\Rightarrow P_{Q}=2 P A=2 \sqrt{12}$

Now, area of $\Delta \mathrm{PQB}=\frac{1}{2} \times \mathrm{PQ} \times \mathrm{AB}$

$=\frac{1}{2} \times 2 \sqrt{12} \times 12$

$=12 \sqrt{12}$

$=24 \sqrt{3}$


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