- #1

- 622

- 281

- Homework Statement
- what is the perimeter of the triangle ABC?

- Relevant Equations
- ##\angle A+\angle B + \angle C = \pi##

Hello, so I saw this problem on a website while looking up trigonometric identities and trying to solve it.

what I know:

The internal angles add up to pi

Let the tangent point between A and B be X

Let the tangent point between B and C be Y

Let the tangent point between C and A be Z

## \overline {AC} = 14##

## \overline {BX} = 16##Things I suspect are true, but have yet to prove:

##\overline {AX} =\overline {AZ}##

##\overline {CZ} =\overline {CY}##

##\overline {BX} =\overline {BY}##

Relations:

##\overline {CY}=14-\overline {AZ}##

##\overline {AX}=\overline {AB}-16##so far I only found three unknowns and only two equations! I think that this is strangely difficult.

what I know:

The internal angles add up to pi

Let the tangent point between A and B be X

Let the tangent point between B and C be Y

Let the tangent point between C and A be Z

## \overline {AC} = 14##

## \overline {BX} = 16##Things I suspect are true, but have yet to prove:

##\overline {AX} =\overline {AZ}##

##\overline {CZ} =\overline {CY}##

##\overline {BX} =\overline {BY}##

Relations:

##\overline {CY}=14-\overline {AZ}##

##\overline {AX}=\overline {AB}-16##so far I only found three unknowns and only two equations! I think that this is strangely difficult.