In the circle given below,

Question:

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

Solution:

$\mathrm{OC}=\frac{13}{2}=6.5$

$\mathrm{AC}=\mathrm{CO}-\mathrm{AO}$

$=6.5-1$

$=5.5$

In $\Delta \mathrm{PAC}$

$\mathrm{PA}=\sqrt{6.5^{2}-5.5^{2}}$

$P A=\sqrt{12}$

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

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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