Answer:
AG = 4
AH = 21
EC = 12
CH = 5
HE = 7
Step-by-step explanation:
The complete question is
The diameters of circles A, C and E are 32 cm, 24 cm and 14 cm respectively.
Which of the following statements are true? Select all that apply.
•AG = 4
•GC = 10
•AH = 21
•EC = 12
•EH = 5
•CH = 5
•HE = 7
The picture of the question in the attached figure
Verify each statement
1) AG = 4
we know that
[tex]AG=AC-GC[/tex]
[tex]AC=32\2=16\ cm[/tex] ----> radius of circle A
[tex]GC=24/2=12\ cm[/tex] ----> radius of circle C
substitute
[tex]AG=16-12=4\ cm[/tex]
therefore
The statement is true
2) GC = 10
we know that
[tex]GC=24/2=12\ cm[/tex] ----> radius of circle C
therefore
The statement is false
3) AH = 21
we know that
[tex]AH=AC+CH[/tex]
we have
[tex]AC=16\ cm[/tex] ----> radius of circle A
[tex]CH=CE-HE[/tex]
[tex]CE=12\ cm[/tex] ----> radius of circle C
[tex]HE=14/2=7\ cm[/tex] ----> radius of circle E
so
[tex]CH=12-7=5\ cm[/tex]
[tex]AH=16+5=21\ cm[/tex]
therefore
The statement is true
4) EC = 12
we know that
[tex]EC=24/2=12\ cm[/tex] ----> radius of circle C
therefore
The statement is true
5) EH = 5
we know that
[tex]EH=14/2=7\ cm[/tex] ----> radius of circle E
therefore
The statement is false
6) CH = 5
we know that
[tex]CH=CE-HE[/tex]
[tex]CE=12\ cm[/tex] ----> radius of circle C
[tex]HE=14/2=7\ cm[/tex] ----> radius of circle E
so
[tex]CH=12-7=5\ cm[/tex]
therefore
The statement is true
7) HE = 7
we know that
[tex]HE=14/2=7\ cm[/tex] ----> radius of circle E
therefore
The statement is true
