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To find the radius of the circle, we can use the relationship between the radius, the chord, and the perpendicular distance from the center of the circle to the chord.
Let:
– ( r ) be the radius of the circle,
– ( d ) be the perpendicular distance from the center to the chord, which is 15 cm,
– ( c ) be half the length of the chord, which is ( frac{40}{2} = 20 ) cm.
We can use the Pythagorean theorem in the right triangle formed by the radius, the half chord, and the perpendicular distance:
[
r^2 = d^2 + c^2
]
Substituting the values:
[
r^2 = 15^2 + 20^2
]
[
r^2 = 225 + 400
]
[
r^2 = 625
]
[
r = sqrt{625}
]
[
r = 25 text{ cm}
]
Thus, the radius of the circle is 25 cm.