Question

Find the value of k in the following figure.

Answer 1

3(k+3)=5(5+6)

3k+9=55

3k=46

k =
`(46)/(3)` = 15 1/3

Answer 2

From the secant theorem we know that:

`3\cdot(3+k)=5\cdot(5+6)\\\\9+3k=5\cdot11\\\\9+3k=55\\\\3k=55-9\\\\3k=46\qquad|:3\\\\\boxed{k=15(1)/(3)}`