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Find the maximum number of distinct regions into which the area inside a circle can be divided by drawing six chords.

Question

Find the maximum number of distinct regions into which the area inside a circle can be divided by drawing six chords.

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Solution

To solve this problem, we can use the formula for the maximum number of regions R that can be divided by n chords. The formula is:

R = n^2 - n + 2 / 2

Step 1: Substitute n = 6 into the formula.

R = 6^2 - 6 + 2 / 2

Step 2: Simplify the equation.

R = 36 - 6 + 2 / 2

Step 3: Continue to simplify.

R = 32 / 2

Step 4: Solve for R.

R = 16

So, the maximum number of distinct regions into which the area inside a circle can be divided by drawing six chords is 16.

This problem has been solved

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