The value of length HL is 8.
How to find HL when two secant intersect outside a circle?
A secant is a line that intersects a circle in exactly two points
When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other.
Therefore,
(EF + FL)FL = HL(GH + HL)
(10 + 14)10 = (HL + 30 - HL)HL
240 = 30(HL)
divide both sides by 30
Hence,
240 / 30 = 30HL / 30
8 = HL
Therefore,
HL = 8
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