 Hello and welcome to problem-solving session on triangles in this question it's given that ad is the bisector of angle a and BT bd is four centimeter DC is three centimeter and AB is six centimeter These are the info mission, which is given we have to determine the length of AC. So this is what? Okay, so let us say AC's length is X. I can always say and What's given? So let's do it methodically. So given is ad is the bisector ad is the bisector bisector of Triangle, sorry angle B AC now. This is good enough hint In terms of what exactly is to be done in this question. So ad is bisector, which is hinting that we have to use angle bisector theorem, right and what is to find? To find AC and I'm calling it X Right now solution how to solve this so by Angle bisector theorem In fact internally you should also write internal angle bisector theorem because we have also seen There is an external angle bisector theorem as well. So by angle bisector theorem and as I mentioned you can mention internal Right internal angle bisector theorem. We know that AB upon AC is equal to BD upon DC no problem in this so this implies AB we know this is six and AC is that's what we have to find out and BD is four and DC is three. I'm not writing the units because all the units will get cancelled So X becomes six into three upon Four now, this is two times three two times two. So this is nine by two nine by two that is four point five Centimeter very very straightforward question, isn't it just the theorem is given or the triangle is given One side is given and the two divisions made by the angle bisector is given You have to find out the other adjacent side. So direct application of Angle bisector theorem. I hope you understood this. So straightforward question Here is another question guys. It says AD is the bisector of angle BAC and AB is given 10 centimeter AC is 14. So let me highlight it AC is 14 a B is 10 BC is given as six. So this entire thing here is six and We have to find BD that is X and DC which is six minus X obviously So again What's given? So given is AD is the bisector by sector of Angle BAC Correct and because of that what will happen? We know by angle bisector theorem By internal again, you have to use internal Angle by sector Internal angle bisector theorem. What do we know? We know that AB upon AC Will be equal to BD upon DC, isn't it? So again a very direct question, you know So hence let's write AB as 10 because it's given as 10 AC is given to be equal to 14 and this is what X upon 6 minus X Right. This is what would be the relationship. So if you cross multiply you'll get 10 times 6 minus X is equal to 14 times X So from here, what do we see? We see 60 minus 10 X is equal to 14 X So if you simplify this will become 24 X Is equal to 60 so X is equal to 60 upon 24 so 12 times 2 and this is 5 So 5 upon 2 that means X is 2.5 centimeter that is BD is 2.5 centimeter. So clearly DC is equal to 6 minus X so it will become 3.5 centimeter, isn't it and just for the You know mentioning we have to mention X is equal to 2.5 centimeters, so these were the two demand of the question right BD and DC So we now know DC is this much BD is this much so hence done again in these two questions We saw it's very you know in the direct application of internal angle bisector theorem