Question

Line segments MP and ML are perpendicular chords in circle O. MP = 10 and ML = 24.

Triangle L M P is inscribed within circle O. The length of M P is 10 and the length of M L is 24. Angle P M L is a right angle.

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 1

True:
- The radius of circle O is 13. (LP = √(10^2 + 24^2) = 26, so radius = 26/2 = 13.)
- LP is a diameter of circle O. (A right angle subtends a diameter — Thales' theorem, so the hypotenuse LP is the diameter.)
- ∠LMP intercepts a semicircle. (Since LP is a diameter, the intercepted arc LP is a semicircle.)

False:
- The diameter is 34. (Diameter is 26, not 34.)
- The measure of arc LP is 90°. (Arc LP is 180°, not 90°.)