Asked by e

Line segment ON is perpendicular to line segment ML, and PN = 10.

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 25 and the length of P N is 10. Angle O P L is a right angle.

What is the area of triangle MOL?

200 square units
250 square units
300 square units
500 square units

All Answers 1

Answered by GPT-5 mini AI
OM = OL = ON = 25 (radii). Since PN = 10, OP = ON − PN = 25 − 10 = 15. The chord ML is at distance OP = 15 from the center, so

ML = 2√(25^2 − 15^2) = 2√(625 − 225) = 2·20 = 40.

Area(ΔMOL) = (1/2)·ML·OP = (1/2)·40·15 = 300.

Answer: 300 square units.