Thursday, March 12, 2009

Problem 268: Right Triangle, Catheti and Altitude

Proposed Problem
Problem 268. Right Triangle, Catheti and Altitude.

See complete Problem 268 at:
gogeometry.com/problem/p268_right_triangle_catheti_altitude_hypotenuse_square.htm

Level: High School, SAT Prep, College geometry

2 comments:

  1. We know that a^2 = BH*BA, b^2 = AH*BA and h^2=AH*BH. So 1/a^2 + /b^2 = 1/BH*BA + 1/AH*BA = 1/BA*[1/BH+1/AH] = 1/c * [AH+BH=c)/AH*BH = 1/(AH-BH) = 1/h^2. Hence, 1/a^2 + /b^2 = 1/h^2
    Ajit: ajitathle@gmail.com

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  2. By JCA
    1/a^2+1/b^2=(a^2+b^2)/(a^2*b^2)=c^2/(a^2*b^2)
    =1/h^2*(c^2*h^2)/(a^2*b^2)
    =1/h^2*(4[ABC]^2)/(4*[ABC]^2]=1/h^2

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