what is the value of n?

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n =
cm

 n=8 cm

Step-by-step explanation:

You can solve this problem by applying the "Intersecting chords theorem". You must follow the proccedure below:

 1. Let's represent each length, as below:

 (P will be the point of intersection)

 AP=4 cm

 CP=6 cm

 DP=3 cm

 BP=n

 2. Therefore, you have:

 APxCP=BPxDP

 APxCP=nxDP

 3. Now, you must clear "n", as below:

 n=APxCP/DP

 4. When you substitute each value into n=APxCP/DP, you obtain:

 n=(4 cm)(6 cm)/3 cm

 n=24 cm²/3 cm

 5. Finally, the result is:

 n=8 cm