Question

Need help! Does anyone know how to do this type of math? (It's geometry)

Answer 1

71

Explanation:

refer the attachment

to solve the question we need to recall one of the most important theorem of circle known as two tangent theorem which states that tangents which meet at the same point are equal that is being said

• FA=AI=17
• CH=CG=2.5

since
`\rm BA=FA+FB` and it's given that FA and BA are 17 and 29 FB should be

• 
  `\rm 29=17+FB`

therefore,

• 
  `FB=29-17=\boxed{12}`

once again by two tangent theorem we acquire:

• 
  `FB=BH=\boxed{12}`

As BC=BH+CH,BC is

• 12+2.5
• 
  `\boxed{14.5}`

likewise,AD=AI+DI so,

• 21=17+DI [AD=21(given) and AI=17 (by the theorem)]

thus,

• DI=21-17=
  `\boxed{4}`

By the theorem we obtain:

• DI=DG=4

Similarly,DC=DG+CH therefore,

• DC=4+2.5=
  `\boxed{6.5}`

Now finding the Perimeter of ABCD

• 
  `P_{\text{ABCD}}=\text{AB+AD+BC+DC}`

substitute what we have and got

• 
  `P_{\text{ABCD}}=\text{29+21+14.5+6.5}`

simplify addition:

• 
  `P_{\text{ABCD}}=\boxed{71}`

hence,

the Perimeter of ABCD is 71