Problem of Squares
Geometry
Level
pending
ABCD is a square in which AC is the diagonal. Any line segment XY cuts AB at X and BC at Y such that XYllAC. If length of Square is 8cm and length of BY is 2cm, then value of AX+BY ?
The answer is 8.
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1 solution
from B draw a perpendicular to AC such that it cuts AC at M and XY at N
So, angle MBC=angle MBA. (RHS)
now,
triangle XBN congruent to triangle YBN (SAS, also angle BNY=90*)
So, BX=BY
=>BX=2cm.
=>AX=6cm
therefore AX+BY=6+2=8cm