Math, asked by kartiknamdev1234, 4 months ago

15. In AABC, AB=AC and CP 1 AB. Prove that
(i) 2AB.BP = BC2 (ii) CP2 - BP2 = 2AP.BP
P Р
B В
C​

Answers

Answered by Anonymous
10

Answer:

ANSWER

ABC is a isosceles triangle in which AB=AC

BD Perpendicular to AC

In △ABD

AB

2

=AD

2

+BD

2

...(Pythagoras theoram)

∴AC

2

=AD

2

+BD

2

....(as AB=AC) ...(1)

From diagram, we see that

⇒AC=CD+AD

⇒AC

2

=(CD+AD)

2

From (1) we get,

⇒(CD+AD)

2

=AD

2

+BD

2

CD

2

+AD

2

+2(CD×AD)=AD

2

+BD

2

CD

2

+2(CD×AD)=BD

2

...(AD square gets cancelled from both sides)

BD

2

−CD

2

=2(CD×AD)

Hence proved.

OK. thanks... rih

ght

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