Question

Circle E has a radius of 5.3 meters.

F

G

¯

is a chord and

H

E

↔

is a perpendicular bisector of

F

G

¯

. If FG = 7.3 meters, calculate the distance of IH .

Answer 1

1.46m

Explanation:

construction ; join EF

we know that EF is a radius, so EF = 5.3m

In triangle EFH,

∡EHF = 90° (EH is the perpendicular bisector of GF)

FH = FG/2 = 7.3m / 2 = 3.65m (EH is the perpendicular bisector of GF)

According to pythagoras theorem,

FH² + EH² = EF²

3.65² + EH² = 5.3²

EH² = 5.3² - 3.65²

EH² = 28.09 - 13.32 = 14.77m

EH = √14.77m

EH = 3.84m

EI is a radius, so EI = 5.3m

IH = EI - EH

= 5.3m - 3.84m

= 1.46m