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Find the relation between BC^3 and BD^3+BE^3

Source: MTRP 2015 Class 11-Multiple Choice Question: Problem 8 :-

September 21, 2020

geometry

Problem Statement

\triangle A B C

A B=A C

and

D

is foot of the perpendicular from

C

A B

and

E

the foot of the perpendicular from

B

A C,

then
[*]

BC^3>BD^3+BE^3

[*]

BC^3 <BD^3+BE^3

[*]

BC^3=BD^3+BE^3

[*] None of these