line segment on is perpendicular to line segment ml. what is the length of segment np? 1 unit 2 units 3…

Answer:

3 units

Explanation:

Step1: Apply the geometric - mean theorem

In a right - triangle formed by the radius, the perpendicular from the center to the chord, and half of the chord, if we consider right - triangle $\triangle{OLP}$ and $\triangle{NLP}$. Let $OP = 4$ and $OL=5$. Since $ON\perp ML$, by the Pythagorean theorem in $\triangle{OLP}$, we can find $LP$. In right - triangle $\triangle{OLP}$, $LP=\sqrt{OL^{2}-OP^{2}}$. [LP=\sqrt{5^{2}-4^{2}}=\sqrt{25 - 16}=\sqrt{9}=3] In right - triangle $\triangle{NLP}$, because of the properties of chords and perpendiculars from the center of a circle, $NP = LP$. So $NP = 3$ units.