Question

Line segment ON is perpendicular to line segment ML.

Circle O is shown. Line segments O L, O N, and O M are radii. A line is drawn from point M to point L and it intersects line O N at point P to form a right angle. The length of O L is 5 and the length of M P is 4.

What is the length of segment NP?

1 unit
2 units
3 units
4 units

Answer 1

If ON is perpendicular to chord ML, then the radius ON (through the center O) bisects the chord, so P is the midpoint of ML. Thus LP = MP = 4, so half the chord = 4. The distance from O to the chord is OP = sqrt(5^2 − 4^2) = sqrt(25 − 16) = 3. Since ON = 5, NP = ON − OP = 5 − 3 = 2.

Answer: 2 units.