Math, asked by navyasangeet922, 11 days ago

ABC is a triangle with AB = AC and right angled at A. Bisector of angle A meets BC at D. Then, BC = ______

Answers

Answered by 22122006
0

Answer:

2AD

Step-by-step explanation:

In ΔABD and ΔACD

AB=AC (given)

∠BAD=∠CAD

As AD is bisector of ∠A and AD=AD

ΔDAB=ΔDAC (by SAS congruency rule)

∠ADB=∠ADC (by c.p.c.t)

∠ADB=∠ADC=90

0

and BD=DC

In ΔABD,

AD

2

+BD

2

=AB

2

…(i)

AD

2

+DC

2

=AC

2

…(ii)

Adding (i) and (ii), we get

2AD

2

+BD

2

+DC

2

=AB

2

+AC

2

2AD

2

+BD

2

+DC

2

=BC

2

2AD

2

+2BD

2

=BC

2

2(AD

2

+BD

2

)=BC

2

2[AD

2

+(

2

1

BC)

2

]=BC

2

2[AD

2

+

4

1

BC

2

]=BC

2

2AD

2

+

2

1

BC

2

=BC

2

2AD

2

=BC

2

2

1

BC

2

=

2

BC

2

4AD

2

=BC

2

2AD=BC

i.e. BC=2AD

Hence proved.

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