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What is the perimeter of a right triangle such that the hypotenuse is 17 units and a circle with a radius of 2 is inscribed within the triangle?
kyky16 · 22-25, F
Yea no it’s too late for all that where I’m from lol@stound
@kyky16 oh.
kyky16 · 22-25, F
I’m just not in the mood to answer that lol@stound
@kyky16 fair point
This message was deleted by its author.
This message was deleted by its author.
AndyC · 22-25, F
@stound

I tried, but I only got here ... hahaha.

I was thinking of getting the perimeter through the area of the triangle ... but something tells me that the radius of the circumference is the key to knowing one of the legs of the triangle. To then apply the Pythagorean Theorem
JoyfulSilence · 46-50, M
The answer is 38.

I drew a diagram.


Given this diagram, we have 4 small triangles
1 = P, C, L
2 = M, C, L
3 = P, C, R
4 = N, C, R

Then A+B = distance from L to R, which is 17.

Triangle 1 has legs of length A and 2.
Triangle 2 has legs of length X-2 and 2.
Both have the same hypotenuse.
So A^2 + 4 = (X-2)^2 + 4,
Or X = A + 2

Triangle 3 has legs of length B and 2.
Triangle 4 has legs of length Y-2 and 2.
Both have the same hypotenuse.
So B^2 + 4 = (Y-2)^2 + 4,
Or Y = B + 2

The perimeter is
X + Y + 17
= ( A + 2 ) + ( B + 2 ) + 17
= ( A + B ) + 2 + 2 + 17
= ( A + B ) + 21
= 17 + 21
= 38

QED.
JoyfulSilence · 46-50, M
I edited my reply to fix typos and errors. So you might want to read it again.
AndyC · 22-25, F
@JoyfulSilence I'm reading it... translating it to Spanish and doing the excersice step by step.
JoyfulSilence · 46-50, M
@AndyC @stound I just drew a diagram in MS Paint:

JoyfulSilence · 46-50, M
@stound @AndyC I added the diagram to my original reply, and deleted all the text that described the diagram.