Question

From a point P(16, 7), tangent PQ and PR are drawn to the circle $x^2+y^2-2x-4y-20=0$. If C be the center then area of the quadrilateral PQCR will be-

• A. 75
• B. 150
• C. 15
• D. None of these

Answer 1

The correct option is A 75

We have,

Equation of circle is

$x^2+y^2-2x-4y-20=0$

From the point $P(16,7)$

According to given question and figure

Now,

$ar\left(\square PQCR\right)=2\Delta PQC$

Because $\Delta PQC=\Delta PRC$

$ar\left(\square PQCR\right)=2\Delta PQC=2\times \frac{1}{2}\times L\times r$

Now

$L=\sqrt{S_1}=15$

$r=\sqrt{g^2+f^2-c}$

$r=\sqrt{1+4+20}=\sqrt{25}$

$r=5$

Then,

$ar\left(\square PQCR\right)=2\Delta PQC=2\times \frac{1}{2}\times 15\times 5$

$ar\left(\square PQCR\right)=75\text{sq}\text{.}\text{units}$

Hence, this is the answer.