Proposed Problem

See complete Problem 268 at:

gogeometry.com/problem/p268_right_triangle_catheti_altitude_hypotenuse_square.htm

Level: High School, SAT Prep, College geometry

## Thursday, March 12, 2009

### Problem 268: Right Triangle, Catheti and Altitude

Labels:
altitude,
cathetus,
hypotenuse,
right triangle

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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

ReplyDeleteAjit: ajitathle@gmail.com

By JCA

ReplyDelete1/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