All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Constant Ratio (Posted on 2013-12-17) Difficulty: 2 of 5

  
A circle has diameter AB and a point P lies on AB between A and B.
A point X, distinct from A and B, lies on the circle.

Prove that tan(∠AXP)/tan(∠XAP) is constant for all values of X.
  

  Submitted by Bractals    
Rating: 4.0000 (1 votes)
Solution: (Hide)

  
Let Q be the foot of the perpendicular from P to AX.

    tan(∠AXP)     tan(∠QXP)     |QP|/|QX|     |QA|
   ----------- = ----------- = ----------- = ------
    tan(∠XAP)     tan(∠QAP)     |QP|/|QA|     |QX|

                  |AP|
               = ------
                  |PB|
QED
  

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPossible approachbroll2013-12-17 22:42:21
SolutionSolutionHarry2013-12-17 17:17:20
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information