Intersection + tangents

Given a circle with a radius r = 4 cm and a point A for which |AS| applies = 10 cm. Calculate the distance of point A from the intersection of the points of contact of the tangents drawn from point A to the circle.

Final Answer:

x =  8.4 cm

Step-by-step explanation:

$$\begin{gathered} r=4\text{cm} \\ c=10\text{cm} \\ \angle STA=90{}^{\circ } \\ {c}^2=r^2+b^2 \\ b=\sqrt{c^2-r^2}=\sqrt{10^2-4^2}=2\sqrt{21}\text{cm}\doteq 9.1652\text{cm} \\ {r}^2=c\cdot c_1 \\ {c}_1=r^2/c=4^2/10=\frac{8}{5}=1.6\text{cm} \\ x=c-c_1=10-1.6=8.4\text{cm} \end{gathered}$$

Try another example