ABC is a right triangle, right angled at A and D is mid point of AB. Prove that, BC²=CD²+3BD²
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In triangle ABC
By pythagoras theorem
BC²=AB²+AC²....(1)
In triangle ADC
CD²=AC²+AD²
AC²=CD²-AD²
from (1)
BC²=AB²+CD²-AD²
BC²=(AD+BD)²+CD²-AD²
BC²=AD²+2AD.BD+BD2+CD²-AD²
BC²=2AD.BD+BD²+CD²
since D is a midpoint of AB
AD=BD
BC²=2BD²+BD²+CD²
BC²=3BD²+CD²
Hence Proved.....
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