In Triangle ABC, AB=AC and CP is perpendicular to AB.
Prove that
(1) 2AB.BP = BC^2
Answers
Answered by
4
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.
Similar questions