The side BC of a square ABCD is produced to any point E. Prove that AE^2 =2BC.BE + CE^2
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195
HELLO DEAR,
Given: ABCD is a square in which BC is extended.
IN Δ ABE, <B = 90°
[By Pythagoras theorem]
AE² = AB² + BE²
= AB² + (BC + CE)² [as BE = BC + CE]
= AB² + BC² + CE² + 2BC·CE
= CE² + AB² + BC² +2BC·CE
= CE² + BC² + BC² +2BC·CE [AB = BC as ABCD is a square]
= CE² + 2BC² + 2BC·CE
= CE² + 2BC(BC + CE)
= CE² + 2BC·BE
HENCE, AE² = 2BC·BE + CE²
I HOPE ITS HELP YOU DEAR,
THANKS
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