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

Find the length of KB¯¯¯¯¯¯¯¯+AK¯¯¯¯¯¯¯¯. A. 28B. 35C. 21D. 33-example-1
User Gespinha
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1 Answer

9 votes
9 votes

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.

User Stoogy
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3.1k points