In a triangle ABC angle A =90 CA= AB Prove that : DC^2 - BD^2 =2 AB AD - Maths - Triangles

Question

In a triangle ABC angle A =90?
CA= AB
Prove that : DC^2 - BD^2 =2?AB?AD

Sneha Apar · Accepted Answer

Dear student,

Assuming your question to be,

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_558efa59c6002%20png">
In∆ACDapplying Pythagoras theoremCD2=AC2+AD2CD2=AC2+AB+BD2CD2=AC2+AB2+BD2+2AB
BDCD2-BD2=BC2+2AB AD-ABCD2-BD2=BC2-2AB2+2AB
AD       
1from ∆ABC,BC2 = AC2+AB2   Pythagoras theoremBC2 = AB2 + AB2    as, AB = ACBC=2ABNow, from 1, CD2-BD2=2AB2-2AB2+2AB
ADCD2-BD2=2AB AD

Regards

In a triangle ABC angle A =90? CA= AB Prove that : DC^2 - BD^2 =2?AB?AD

In a triangle ABC angle A =90?
CA= AB
Prove that : DC^2 - BD^2 =2?AB?AD