line segments mp and ml are perpendicular chords in circle o. mp = 10 and ml = 24. which statements about…
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 34. lp is a diameter of circle o. ∠lmp intercepts a semicircle. the measure of arc lp is 90°.
Answer
Explanation:
Step1: Apply the Pythagorean theorem
Since MP and ML are perpendicular chords, triangle LMP is a right - triangle with MP = 10 and ML = 24. By the Pythagorean theorem (LP^{2}=MP^{2}+ML^{2}). So (LP=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26).
Step2: Analyze circle properties
The diameter of the circle is the length of the chord that passes through the center. In right - triangle LMP inscribed in the circle, the hypotenuse LP is a diameter of the circle O (a right - triangle inscribed in a circle has its hypotenuse as the diameter). The radius (r=\frac{LP}{2}=\frac{26}{2}=13). Also, (\angle LMP = 90^{\circ}), and an angle inscribed in a semi - circle is a right - angle, so (\angle LMP) intercepts a semi - circle.
Answer:
The radius of circle O is 13. (\overline{LP}) is a diameter of circle O. (\angle LMP) intercepts a semi - circle.