Question

The diameter of circles A,C and E are 32 cm, 24cm and 14 cm respectively

Which of the following statements are true? Select all that apply

Answer 1

AG = 4

AH = 21

EC = 12

CH = 5

HE = 7

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

`AG=AC-GC`

`AC=32\2=16\ cm` ----> radius of circle A

`GC=24/2=12\ cm` ----> radius of circle C

substitute

`AG=16-12=4\ cm`

therefore

The statement is true

2) GC = 10

we know that

`GC=24/2=12\ cm` ----> radius of circle C

therefore

The statement is false

3) AH = 21

we know that

`AH=AC+CH`

we have

`AC=16\ cm` ----> radius of circle A

`CH=CE-HE`

`CE=12\ cm` ----> radius of circle C

`HE=14/2=7\ cm` ----> radius of circle E

so

`CH=12-7=5\ cm`

`AH=16+5=21\ cm`

therefore

The statement is true

4) EC = 12

we know that

`EC=24/2=12\ cm` ----> radius of circle C

therefore

The statement is true

5) EH = 5

we know that

`EH=14/2=7\ cm` ----> radius of circle E

therefore

The statement is false

6) CH = 5

we know that

`CH=CE-HE`

`CE=12\ cm` ----> radius of circle C

`HE=14/2=7\ cm` ----> radius of circle E

so

`CH=12-7=5\ cm`

therefore

The statement is true

7) HE = 7

we know that

`HE=14/2=7\ cm` ----> radius of circle E

therefore

The statement is true