CBSE Class 10 Answered
In an
equilateral triangle ABC, D is a point on side BC such that
BC. Prove that
9AD2 = 7AB2.
![](http://images.topperlearning.com/topper/questions/209891_image147.gif)
Asked by Topperlearning User | 04 Jun, 2014, 13:23: PM
Draw
AP BC.
BD
=
Since
ABC is equilateral and AP
BC,
BP
= PC = BC =
AB
Using
Pythagoras theorem in ABP,
AP2 + BP2 = AB2
AP2
= AB2 - BP2 = AB2 - =
… (1)
Using
Pythagoras theorem in ADP,
AD2 = AP2 + DP2
= AB2
+ (BP - BD)2
= AB2
+
=
36AD2 = 28AB2
9AD2 = 7AB2
Hence, proved.
Answered by | 04 Jun, 2014, 15:23: PM
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