Question

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

Answer 1

`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`