Based on the equidistant chords theorem, the value of m and n in the circle are:
m = 7/4 = 1.75
n = 1/2 = 0.5
What is the Equidistant Chords Theorem?
The equidistant chords theorem states that, two chords are congruent if they are equidistant to the center of the same circle.
Given:
- US = 3m + 2
- RU = -m + 9
- PO = 20 - 14
- EW = -2(2m + 1)
Thus, since US = RU, therefore chords PO and EW are congruent based on the equidistant chords theorem.
Therefore:
3m + 2 = -m + 9
Add like terms
3m + m = -2 + 9
4m = 7
m = 7/4
m = 1.75
20n - 14 = -2(2n + 1)
20n - 14 = -4n - 2
20n + 4n = 14 - 2
24n = 12
n = 12/24
n = 1/2 = 0.5
Therefore, based on the equidistant chords theorem, the value of m and n in the circle are:
m = 7/4 = 1.75
n = 1/2 = 0.5
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