## in triangle ABC , angle C= 90 and AD , BE are medians through A and B respectively prove that 4AD^2=4AC^2+ BC^2

Question

in triangle ABC , angle C= 90 and AD , BE are medians through A and B respectively prove that 4AD^2=4AC^2+ BC^2

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1 month 2021-08-12T12:01:03+00:00 2 Answers 0 views 0

1. Step-by-step explanation:

ABC is a right angled triangle in which angle A=90° and AD is perpendicular

to BC. Thus , In right angled triangle ABC , AB^2+AC^2=BC^2……………(1)

by adding the eqn. (2) and (3)

2.AD^2+DB^2+DC^2= AB^2+AC^2. , putting AB^2+AC^2=BC^2 from eqn. (1)

Second -Method:-

In right angled triangle ABC let angle ABC= B then angle ACB= 90°-B .

Thus , in right angled triangle ADC , angle CAD = B.

In right angled triangle CDA. , tanB=CD/AD………………..(2)

From eqn. (1) and (2)