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Thread: Yet Another Math Problem

  1. #1
    World Champ ODH's Avatar
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    Default Yet Another Math Problem

    Still waiting for Homer's repsonse on his Math problem, so I will post my own.

    What is the radius of a circle inscribed in a 3,4,5 triangle?


    I think this is one of the best problems I have ever seen. There are several different ways to solve it (I know at least four). I have used this questions many times when interviewing Engineers from top schools and they have always struggled.

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    Mayor of Bringsburg homerdindon's Avatar
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    Default Re: Yet Another Math Problem

    Oops, totally forgot about the ant problem with all of the Simpson getting fired stuff going on. I'll revisit now. Oh, and I'll try to figure this one out without cheating. Seems like a good problem.

  3. #3
    Mayor of Bringsburg homerdindon's Avatar
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    Default Re: Yet Another Math Problem

    Ok, is it 1? To get this, I'm assuming that if you draw a radius to the point on the triangle where the circle meets the triangle, that it always forms a right angle.

    EDIT: Ok, I'm dumb. I was thinking of the triangle as a whole, and not each side as a separate line tangent to the circle. Pretty sure that the radius of a circle to a line tangent to the circle always form a right angle, so I'm pretty sure my answer above is correct.
    Last edited by homerdindon; 08-30-2007 at 07:10 PM.

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    Default Re: Yet Another Math Problem

    Quote Originally Posted by homerdindon View Post
    Ok, is it 1? To get this, I'm assuming that if you draw a radius to the point on the triangle where the circle meets the triangle, that it always forms a right angle.

    EDIT: Ok, I'm dumb. I was thinking of the triangle as a whole, and not each side as a separate line tangent to the circle. Pretty sure that the radius of a circle to a line tangent to the circle always form a right angle, so I'm pretty sure my answer above is correct.
    You are right with your answer and that the radius drawn to the tanget point is perpindicular to the tangent line. I do not think that actually proves your answer though

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    Default Re: Yet Another Math Problem

    "I have used this questions many times when interviewing Engineers from top schools and they have always struggled."

    What a pri....

  6. #6
    Mayor of Bringsburg homerdindon's Avatar
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    Default Re: Yet Another Math Problem

    K, I'll try to explain as well as I can.

    Well the area of the big triangle is obviously 6. Don't think that needs any explaining.

    First I drew the radius to each side of the triangle. I figured that you had to somehow find the known area of the big triangle in terms of 'r' and solve for 'r'. Took a few minutes to figure out that I'd somehow have to divide the triangle into sections. Played around with a few things and saw that if you drew a line from each vertex (think it's called vertex, my geometry vocab isn't as sharp as it once was) to the center of the circle, it made perfect little triangles with each radius as the height of the triangle. So adding the 3 triangles up gives .5(4r)+.5(3r)+.5(5r) = 6 --> 6r =6 --> r=1.

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    Mayor of Bringsburg homerdindon's Avatar
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    Default Re: Yet Another Math Problem

    K, I'll try to explain as well as I can.

    Well the area of the big triangle is obviously 6. Don't think that needs any explaining.

    First I drew the radius to each side of the triangle. I figured that you had to somehow find the known area of the big triangle in terms of 'r' and solve for 'r'. Took a few minutes to figure out that I'd somehow have to divide the triangle into sections. Played around with a few things and saw that if you drew a line from each vertex (think it's called vertex, my geometry vocab isn't as sharp as it once was) to the center of the circle, it made perfect little triangles with each radius as the height of the triangle. So adding the 3 triangles up gives .5(4r)+.5(3r)+.5(5r) = 6 --> 6r =6 --> r=1.

    FWIW, with the pressure of an interview, that would be pretty hard considering they can't have more than a few minutes to figure it out.

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    Default Re: Yet Another Math Problem

    Very good Homer!

    Ryou,
    It is very common, if not expected, to be asked technically challenging questions during an engineering interview. It is not expected for them to get it right immediately, but rather to show their thought process and problem solving ability. This is especially true with recent graduates who have little job experience to discuss. Also, I would let them struggle for a bit and then guide them in the right direction.

    Personally, I always wanted to recommend the candidate who enjoyed the challenge, whether or not they were able to answer the question right away.

  9. #9

    Default Re: Yet Another Math Problem

    It's been a long time since I was in geometry, but if you find the center of each side of the triangle and draw a line perpendicular to it (toward the center of the triangle) you should have the centerpoint of the triangle. From there you can measure back to the sides to find the radius.
    "All my life I have tried to pluck a thistle and plant a flower wherever the flower would grow in thought and mind." -- Abraham Lincoln

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