Math, asked by Laxmihaveri, 3 months ago

In Figure, AD ,BC and BD=CD. Prove that 2CAP=2AB2-BC?.
А
B
D​

Answers

Answered by farhaanaarif84
1

Answer:

Given ABC is a triangle and AD⊥BC.

To prove : 2CA

2

−2.AB

2

+BC

2

proof : BD+CD=BC

3

1

.CD+CD=BC

CD+3CD=3.BC

4CD=3BC

CD=

4

3

.BC⋯(1)

From (1)

BD=

4

3

.BC

BD=

4

BC

⋯(2)

In △ACD,

AC

2

=AD

2

+DC

2

⋯(3)

In △ADB,

AB

2

=AD

2

+BD

2

AD

2

=AB

2

−BD

2

⋯(4)

put (4) in (1)

AC

2

=AB

2

−BD

2

+DC

2

AC

2

=AB

2

−(

4

BC

)

2

+(

4

3

.BC)

2

AC

2

=AB

2

16

BC

2

+

16

9.BC

2

AC

2

=AB

2

+

16

−BC

2

+9BC

2

AC

2

=AB

2

+

16

8.BC

2

AC

2

=AC

2

=

2

2.AB

2

+BC

2

∴2AC

2

=2AB

2

+BC

2

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