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.
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.
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