Answer:
the distance between the two tangent points is 10 cm.
Explanation:
Since the two parallel lines are tangent to the circle, they must be equidistant from the center of the circle.
Let O be the center of the circle, and let AB be the distance between the two tangent points. Then, we have:
AB = 2 * OA
Also, we know that the area of the circle is given by:
A = πr^2
where r is the radius of the circle. Since we are given that the area of the circle is 25π cm^2, we have:
25π = πr^2
Simplifying this equation, we get:
r^2 = 25
Taking the square root of both sides, we get:
r = 5
Now, we can use the fact that the two tangent lines are equidistant from the center of the circle to find AB. Let's draw a diagram:
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B
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A
Since OA is the radius of the circle, we have OA = 5 cm. Therefore:
AB = 2 * OA
= 2 * 5
= 10
So, the distance between the two tangent points is 10 cm.