Circle

Chords $AB$ and $CD$ of a circle when extended meet at point $X$.

$AB = 4 \; cm$, $\;$ $BX = 6 \; cm$, $\;$ $XD = 5 \; cm$

Calculate the length of $CD$.

Since chords $AB$ and $CD$ meet externally at point $X$

$\implies$ $XA \times XB = XC \times XD$

Now, $\;$ $XA = AB + BX = 4 + 6 = 10 \; cm$

and $\;$ $XC = XD + CD = \left(5 + CD\right) \; cm$

$\therefore \;$ We have,

$10 \times 6 = \left(5 + CD\right) \times 5$

i.e. $\;$ $12 = 5 + CD$

$\implies$ $CD = 7 \; cm$