If line ji is a midsegment of triangle fgh, find hg. all measurements in the diagram are in inches.

Length of segment HG=60 inches.

Length of JI=30 inches.

Step-by-step explanation:

Given , if a line JI is a midsegment of triangle FGH.

Triangle midsegment theorem: It states that when a segment formed by joining of midpoints of any two sides of a triangle then it is parallel to III side of triangle and half of its length.

JI is the midsegment , J is the midpoint of side HF and I is the midpoint of GF

Therefore, we have

HJ=JF and GI=IF

2x-3=x+2

By subtracting property of equality

2x-x=2+3

x=5 ( by simplification)

Length of side HG= 11x+5

Length of side HG= inches.

By substituting the value of x

JI=

By using theorem

JI=

JI=30 inches.

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐

the answer

b. they are parallel and will never intersect.