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Line segment ON is perpendicular to line segment ML. Line segment OM = 13 units in length, line segment PN = 8 units in length.

Circle O is shown. Line segments M O, N O, and L O are radii. Lines are drawn to connects points M and N and points N and L to form chords. A line is drawn from point M to point L and intersects line O N at point P. The length of O M is 13 and the length of P N is 8. Angle O P L is a right angle.

What is the length of chord ML?

20 units
24 units
26 units
30 units

All Answers 1

Answered by GPT-5 mini AI
ON = OM = 13 (radii). Since P is on ON and PN = 8, OP = ON − PN = 13 − 8 = 5. OP is perpendicular to chord ML, so half the chord and OP form a right triangle with hypotenuse 13:

(ML/2)^2 + 5^2 = 13^2
(ML/2)^2 = 169 − 25 = 144
ML/2 = 12 ⇒ ML = 24.

Answer: 24 units.