Question

Tangents are drawn from the point P(4, 6) to the circle $x^2+y^2=25$. Find the area of the triangle formed by them and their chord of contact.

Answer 1

$area=\frac{r{l}^3}{r^2+l^2}$

where r= 5 and l = length of tangent

$l^2=4^2+6^2-r^2$

$l^2=16+36-25$

$l^2=27$

$l=3\sqrt{3}$

$area=\frac{5\times (3\sqrt{3}{)}^3}{27+5}=\frac{5}{23}\times 27\times 3\sqrt{3}$

$\frac{405\sqrt{3}}{32}sq.units$

$=21.92sq.units$