area of triangle given angle bisector

[ketanco]

In the figure attached, AN is an angle bisector
Angle CHN is right angle
HN = 8 units
AB = 6 units
What is the area of ABN triangle?
Answer should be 24

I tried doing it from ratio of sides from angle bisector formula but then could not get anywhere

 

[Dr.Peterson]

In the figure attached, AN is an angle bisector
Angle CHN is right angle
HN = 8 units
AB = 6 units
What is the area of ABN triangle?
Answer should be 24

I tried doing it from ratio of sides from angle bisector formula but then could not get anywhere

View attachment 10490

Try first drawing a more accurate diagram (make it an actual angle bisector to get the relationships approximately right). Then construct an altitude to AB, which will be useful in finding the area of ABN. You should see something useful.

 

[mmm4444bot]

… I tried doing it from ratio of sides … but then could not get anywhere

Please familiarize yourself with the forum's guidelines. Thank you!

Next, post a reply and show your attempts, up to the point where you got stuck. If you have some idea about why you're uncertain, please explain that, too. :cool: