line segments mp and ml are perpendicular chords in circle o. mp = 10 and ml = 24.

which statements about circle o are true? select three options.

- the radius of circle o is 13.
- the diameter of circle o is 24.
- lp is a diameter of circle o.
- \angle lmp intercepts a semicircle.
- the measure of arc lp is 90^\circ.

Question

line segments mp and ml are perpendicular chords in circle o. mp = 10 and ml = 24.

which statements about circle o are true? select three options.

- the radius of circle o is 13.
- the diameter of circle o is 24.
- lp is a diameter of circle o.
- \angle lmp intercepts a semicircle.
- the measure of arc lp is 90^\circ.

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", "Thaless Theorem" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Thaless Theorem", "Circle Geometry", "Inscribed Angle Theorem" ] } ## Find the diameter of circle O $$ \begin{aligned} &\angle LMP = 90^\circ \implies LP \text{ is a diameter of circle } O \ &LP = \sqrt{MP^2 + ML^2} = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26 \end{aligned} $$ ## Find the radius of circle O $$ \begin{aligned} &r = \frac{LP}{2} = \frac{26}{2} = 13 \end{aligned} $$ ## Evaluate the statements $$ \begin{aligned} &\text{1. The radius of circle } O \text{ is } 13. \quad (\text{True}) \ &\text{2. The diameter of circle } O \text{ is } 24. \quad (\text{False, it is } 26) \ &\text{3. } \overline{LP} \text{ is a diameter of circle } O. \quad (\text{True}) \ &\text{4. } \angle LMP \text{ intercepts a semicircle.} \quad (\text{True, since } \angle LMP = 90^\circ) \ &\text{5. The measure of arc } LP \text{ is } 90^\circ. \quad (\text{False, it is } 180^\circ) \end{aligned} $$

The radius of circle O is 13.

The diameter of circle O is 24.

LP is a diameter of circle O.

∠LMP intercepts a semicircle.

The measure of arc LP is 90°.

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

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Question

Explanation:

Find the diameter of circle O

Find the radius of circle O

Evaluate the statements

Answer: