Question

The side of BC of a square ABCD is produced to any point E.Prove that AE2 = 2 BC.BE + CE2

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Answer 1

Step-by-step explanation:

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