line segment on is perpendicular to line segment ml.

what is the length of segment np?

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Question

line segment on is perpendicular to line segment ml.

what is the length of segment np?

1 unit
2 units
3 units
4 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [ "Kite Properties" ], "current_concepts": [ "Pythagorean Theorem", "Kite Properties", "Circle Geometry" ] } ## Identify the geometric properties of the figure $$ \begin{aligned} &O \text{ is the center of the circle.}\ &OM = OL = r \quad (\text{radii of the circle})\ &ON \perp ML \text{ at point } P\ &OL = 5, \quad MP = 4 \end{aligned} $$ ## Calculate the length of segment OP $$ \begin{aligned} &OP \perp ML \implies \triangle OPL \text{ is a right triangle at } P\ &PL = MP = 4 \quad (\text{perpendicular from center bisects the chord})\ &OP = \sqrt{OL^2 - PL^2} = \sqrt{5^2 - 4^2} = 3 \end{aligned} $$ ## Calculate the length of segment NP $$ \begin{aligned} &ON = OL = 5 \quad (\text{radius of the circle})\ &NP = ON - OP = 5 - 3 = 2 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties of the figure

Calculate the length of segment OP

Calculate the length of segment NP

Answer: