Chord 2

Point A has a distance of 13 cm from the center of the circle with a radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle.

Correct answer:

x =  9.2308 cm

Step-by-step explanation:

$$\begin{gathered} a=5\text{cm} \\ c=13\text{cm} \\ {b}^2=c^2-a^2 \\ b=\sqrt{c^2-a^2}=\sqrt{13^2-5^2}=12\text{cm} \\ {S}_1=S_2 \\ \frac{ab}{2}=\frac{cv}{2} \\ ab=cv \\ v=\frac{a\cdot b}{c}=\frac{5\cdot 12}{13}=\frac{60}{13}\doteq 4.6154\text{cm} \\ x=2\cdot v=2\cdot 4.6154=\frac{120}{13}\text{cm}=9.2308\text{cm} \end{gathered}$$

Try another example