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Answer :
Final answer:
To find the length of segment QP, use the tangent-segment theorem and the Pythagorean theorem in a right triangle.
Explanation:
To find the length of segment QP, we need to use the tangent-segment theorem. In a circle, a line tangent to the circle is perpendicular to the radius at the point of tangency. Since OP is tangent to circle N at point O, it is perpendicular to radius NO. Therefore, triangle NOP is a right triangle. We can use the Pythagorean theorem to find the length of segment QP. Using the given values, we have:
NO2 + OP2 = NP2
92 + 122 = NP2
81 + 144 = NP2
225 = NP2
NP = 15
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