Answer:
OL = 14 or 10
Explanation:
Let OL = x
ON = LN - OL
= 24 - x
Chord intersecting theorem:
If two chords intersect inside a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
OL * ON = OM * OP
x * (24 - x) = 20 * 7
x*24 - x*x = 140
24x - x² = 140
x² - 24x + 140 = 0
Factors are (-14) and (-10). When we add (-14) and (-10), we get -24 & when we multiply (-14) and (-10), we get 140.
Rewrite the middle term using the factors.
x² - 14x - 10x + 140 = 0
x(x - 14) - 10(x - 14) = 0
(x - 14)(x - 10) = 0
x - 14 = 0 or x - 10 = 0
x = 14 or x = 10
OL = 14 or 10