Answer :
Final answer:
To find the radius of circle O, we can use the given ratio of lengths described in the diagram. By applying the Pythagorean theorem to the triangle formed by qo, qp, and on, we can solve for the radius. Therefore, the radius of circle O is 8 units.
Explanation:
To find the radius of circle O, we can use the given ratio of lengths qn:np = 2:3 and the length of qp = 10. Since qn:np = 2:3, we can say that qn is 2/3 of qp. Therefore, qn = (2/3) * 10 = 6. Now, we can use the Pythagorean theorem to find the length of on, which is the hypotenuse of the right triangle formed by qo, qp, and on. We have qp = 10, qn = 6, and we want to find the length of on, which is the radius of circle O. Using the Pythagorean theorem, we have (on)^2 = (qp)^2 - (qn)^2. Plugging in the values, we have (on)^2 = (10)^2 - (6)^2. Simplifying this, we get (on)^2 = 100 - 36 = 64. Taking the square root of both sides, we find that on = 8. Therefore, the radius of circle O is 8 units.
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