Answer:
see explanation
Step-by-step explanation:
(a)
given 2 intersecting chords in a circle, then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
FH × HG = DH × HE ( substitute values )
2y = 3 × 4 = 12 ( divide both sides by 2 )
y = 6
then
DE = 3 + 4 = 7
FG = 2 + y = 2 + 6 = 8
(b)
given 2 secants from an external point to a circle, then the product of one secant's external part and the entire secant is equal to the product of the other secant's external part and the entire secant , that is
AB × AC = AD × AE ( substitute values )
5(5 + x) = 6 × (6 + 6)
25 + 5x = 6 × 12 = 72 ( subtract 25 from both sides )
5x = 47 ( divide both sides by 5 )
x = 9.4
then
AE = 6 + 6 = 12
AC = 5 + x = 5 + 9.4 = 14.4
