Question

Find the length of KB¯¯¯¯¯¯¯¯+AK¯¯¯¯¯¯¯¯. A. 28B. 35C. 21D. 33

Answer 1

For this problem, we are given a circle with two intersecting chords. We need to determine the sum of the segments KB and AK.

We can use the following identity to solve for x.

$DK\cdot KB=AK\cdot KC$

We have:

$\begin{gathered} 12\cdot(4x+1)=14\cdot(3+3x)\\ \\ 48x+12=42+42x\\ \\ 48x-42x=42-12\\ \\ 6x=30\\ \\ x=5 \end{gathered}$

Now we need to compute the distances:

$KB+AK=14+4\cdot(5)+1=35$

The correct answer is B.