Question

Given the circle below with secant EFG and IHJ find the length of EF round to the nearest 10th if necessary

Answer 1

EF ≈ 23.3

Explanation:

given 2 secants drawn from an external point to the circle.

then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is

GF × GE = GH × GI

8 × GE = 10 × (10 + 15) = 10 × 25 = 250 ( divide both sides by 8 )

GE = 31.25

then

EF = GE - GF = 31.25 - 8 = 23.25 ≈ 23.3 ( to the nearest tenth )