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

In a triangle ABC,B=900,BE=3 and BD=4. If AE=ED=DC, then the value of AC can be expressed as ab, where a,b are positive integers and b is square free. Find a+b.
550961.png

Open in App
Solution

Let CD=DE=EA=x

Applying Apollonius theorem in ABD

BD2+AB2=2{BE2+x2}16+AB2=2(9+x2)AB2=2+2x2 .....(i)

Applying Apollonius theorem in BCE, we have

BE2+BC2=2{BD2+x2}9+BC2=2(16+x2)BC2=23+2x2 .....(ii)

In right angled ABC

AB2+BC2=AC2AB2+BC2=(3x)2 .....(iii)

Substituting values of equations (i) and (ii) in equation (iii), we get

2+2x2+23+2x2=9x225=5x2x=5$

Thus AC=3x=35

We have ab=35

a=3,b=5a+b=8

Hence, the answer is 8.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle Sum Property
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon