8filltheheart Posted January 17, 2013 Share Posted January 17, 2013 A circle is inscribed in a rt triangle. The radius of the circle is 6 cm, and the hypotenuse is 29 cm. Find the lengths of the 2 segments of the hypotenuse that are determined by the pt of tangency. The solutions manual sets up the answer using (35 - x)^2 + (6 + x)^2 = 29^2 I understand the 6+x, but I can't figure out how they got the 35. Thanks Quote Link to comment Share on other sites More sharing options...

jennynd Posted January 17, 2013 Share Posted January 17, 2013 29-x+6 You assume one leg is 6+x. that means the hypotenuse is x +29-x = 29. that means the other leg is 29-x+6 Quote Link to comment Share on other sites More sharing options...

regentrude Posted January 17, 2013 Share Posted January 17, 2013 I call the segments of the hypotenuse x and y. We know x+y=29 Because the triangle is right, Pythagoras holds: a^2+b^2=29^2 with a and b the two sides. Using the inscribed circle, we can express the two short sides as a=x+r and b=9+r (r=6, radius of circle) (sides of triangle are tangent on circle, thus radius makes right angle with side, we see similar triangles...) Now writing Pythagoras: (x+6)^2+(y+6)^2=29^2 Using the first equation, x+y=29, we can express y=29-x Now put in Pythagoras: (x+6)^2+((29-x)+6)^=29^2 so (x+6)^2+(35-x)^2=29^2 Quote Link to comment Share on other sites More sharing options...

8filltheheart Posted January 17, 2013 Author Share Posted January 17, 2013 I call the segments of the hypotenuse x and y. We know x+y=29 Because the triangle is right, Pythagoras holds: a^2+b^2=29^2 with a and b the two sides. Using the inscribed circle, we can express the two short sides as a=x+r and b=9+r (r=6, radius of circle) (sides of triangle are tangent on circle, thus radius makes right angle with side, we see similar triangles...) Now writing Pythagoras: (x+6)^2+(y+6)^2=29^2 Using the first equation, x+y=29, we can express y=29-x Now put in Pythagoras: (x+6)^2+((29-x)+6)^=29^2 so (x+6)^2+(35-x)^2=29^2 Thank you! I didn't think of setting it up as 29=x+y. That makes it perfectly clear. I appreciate the help. Quote Link to comment Share on other sites More sharing options...

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