wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In an isosceles triangle with base a and a lateral side b the vertex angle is equal to 20. Prove that |a|3+|b|3=3|a||b|2.

Open in App
Solution


AC=a AB=BC=b
Let MBC such that AM=a
Hence BAM=800200=600
Now let NAB such that AN=a
Here AN=AM=MN=a and NMB=1800800600=400
Now let kBC such that Nk=a
Then, NkM=400 which says that
BNk=200 and from here Dk=a
Now kLD altitude of ΔBNk and MFD altitude of ΔAMC
Here since BN=ba and ΔBLkΔAFM
we obtain AF=BC=ba2
and FC=aba2=3ab2
Also we see that ΔABCΔACM which gives
MCa=ba or MC=b2a
Since AM2AF2=MC2FC2 we obtain
a3+b3=3ab

1221456_890409_ans_55b2dd5e96d046c4b59145a3e3ee6cf1.jpg

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Criteria for Congruency
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon