Flag 9 grade maths> Given that ABC is an isosceles right tria...
question mark

Given that ABC is an isosceles right triangle with AC=BC and angle ACB=90°.D is a point on AC and E is point on the extension of BD such that AE  is perpendicular to BE. If AE=1/2BD,prove that BD bisects angle ABC.

N Sekhar , 5 Years ago
Grade 12th pass
anser 1 Answers
Aditya Gupta

Last Activity: 5 Years ago

this is an EXTREMELY easy ques. lemme explain.
note that if angle CBD= p, then angle CDB= 90 – p= angle ADE.
since angle AED= 90 (given), so EAD= 180 – (90+90 – p)= p
let AE=a so that BD= 2a
now AC= AD+DC
now ADcosp=AE= a
or AD= asecp
also BDsinp= DC= 2asinp
so AC= AD+DC= asecp+2asinp
but AC= BC
and BC= BDcosp= 2acosp
so asecp+2asinp= 2acosp
or 1+2sinpcosp= 2cos^2p
or sin2p=cos2p
or tan2p=1=tan45
or 2p=45
or p= 22.5
since angle ABC= 45, so p= 45/2 is half of it. thence BD bisects angle ABC.
kindly approve :)

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...