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All sides of ∆ABC are tangent to circle P.
What is the perimeter of triangle ABC?​

User Julieanne
by
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1 Answer

7 votes

Answer:


Perimeter =58

Explanation:

Given


AB = 24

See attachment

Required

The perimeter of ABC

First, calculate the lengths of AC and BC.

From the attachment.


Ax = Az =10


Cx = Cy = 5


By =Bz

So, we have:


AC = 10 + Cx


AC = 10 + 5


AC = 15

Also:


Az + Bz = AB


Az + Bz = 24

Recall that:
Ax = Az =10

So:


10 + Bz = 24


Bz = 24 - 10


Bz = 14

So, we have:


By = Bz = 14

To calculate BC, we have:


BC = 5 + By


BC=5+14


BC = 19

The perimeter is then calculated as:


Perimeter = AB + BC + AC


Perimeter = 24 + 19 + 15


Perimeter = 58

All sides of ∆ABC are tangent to circle P. What is the perimeter of triangle ABC?​-example-1
User Matt Sergeant
by
6.9k points