Circle in a Triangle

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Riot

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Find the perimeter of the triangle at the right. Assume that the line segments are tangent to the circle.

Problem.png

I have no idea what im doing...and I feel bad for asking so many questions o_O i just need an explanation?
 
Riot said:
Find the perimeter of the triangle at the right. Assume that the line segments are tangent to the circle. View attachment 2012
I have no idea what im doing...and I feel bad for asking so many questions o_O i just need an explanation?
Click to expand...
This depends entirely on one fact: Two tangents to a circle from a common point have the same length to the points of contact with the circle.

So one side of the triangle is \(\displaystyle 9+14=23\).

You do some more work.
 
Look at Pappus's picture. One of the green segments has length 9 so the other one does also. Since the base line, with length 15, is made of one green and one red segment so the red segment has length 15- 9= 6. Since we are told that the length of one of the blue segments is 14, the side made of a blue and a red segment and so has length 14+ 6= 20. The third side, then, consisting of the blue and green segments has length 14+ 9= 23.
 
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