If E is a point on side r:A of an equila...

If E is a point on side r:A of an equilateral triangle ABC such that `BE bot CA`, then prove that `AB^(2) +BC^(2) +CA^(2) = 4BE^(2)`.

A

`2BE^(2)`

B

`3BE^(2)`

C

`4BE^(2)`

D

`6BE^(2)`

Verified by Experts

The correct Answer is:

C

TRIANGLES
S CHAND IIT JEE FOUNDATION|Exercise Question Bank|30 Videos
TIME AND WORK
S CHAND IIT JEE FOUNDATION|Exercise Self Assessment Sheet - 20|10 Videos
TRIGONOMETRICAL RATIOS
S CHAND IIT JEE FOUNDATION|Exercise Self Assessment Sheet - 40|1 Videos

Similar Questions

Explore conceptually related problems

A point D is on the side BC of an equilateral triangle ABC such that DC=(1)/(4)BC. Prove that AD^(2)=13CD^(2)

In an equilateral triangle ABC the side BC is trisected at D. Prove that 9AD^(2)=7AB^(2)

In an equilateral triangle ABC,D is a point on side BC such that BD=(1)/(3)BC Prove that 9AD^(2)=7AB^(2)

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.Prove that AE^(2)+BD^(2)=AB^(2)+DE^(2)

Let ABC be an equilateral triangel. Let BE_|_CA meeting CA at E, then (AB^(2)+BC^(2)+CA^(2)) is equal to :

D is a point on the side BC of a triangle ABC /_ADC=/_BAC Show that CA^(2)=CB.CD

If G be the centroid of the Delta ABC, then prove that AB^(2)+BC^(2)+CA^(2)=3(GA^(2)+GB^(2)+GC^(2))

In the given figure , D is a point on the side BC of Delta ABC such that angle ADC=angle BAC . Prove that CA^(2)=CBxxCD .