Students in this video, let's discuss how to find the sock'em center of a triangle if you know the
three vertices of the triangle.
All right.
Now, remember, we have discussed what the Sock'Em Center is.
It's the meeting point of the perpendicular bicyclers of the sides of the triangle.
All right.
Now, there is a special case where we can easily find the Starcom Center.
That's the case of a right angle triangle.
Right.
We have learned something about this which will help us find the sock'em center of a right angle triangle
very quickly now.
We will discuss that later in this video.
We are discussing the general case.
All right.
Now to find the sock'em center, you need to check which point among the four given options is at the
same distance from every vertex of the triangle.
Now, why is that?
So, for example, you have Triangle ABC over here.
Now, if this is the center of this triangle, then with this point as the center, you can draw a circle
that will meet every vertex of the triangle.
Right.
We have discussed that.
And this is called the Circle Circle of the Triangle.
And this is called Issaka Radius right now.
That's why the distance of this point from each of the vertices has to be equal.
If this is all then or is the radius of the circle circle.
Similarly, Albie's the radius of the circle circle and Ossy is the radius of that circle circle.
All right.
So let's proceed.
Let me clear this up.
OK, now say the four vertices that are given to you are zero comma, minus two one comma, minus one,
two, comma one and two comma zero.
Now, the approach should be that you need to find which among these four points is at the same distance
from E, B and C..
All right.
Now, let's start with option one.
What is the distance of zero comma, minus two from one comma for we know how to find the distance when
we know the vertices of two points.
Right.
So you will get the answer.
The square root of thirty seven.
That is root of one square plus six square.
Right.
Why is that.
So you have zero and you have one.
So zero minus one gives you minus one and that's the same as one square.
Right.
And minus two.
Minus four gives you minus six, minus X squared and six squared is the same.
So you're right, six squared over here.
So six squared plus one square gives you thirty seven and ends the distance between point eight.
That's this vertex and this option is route 37.
All right.
Now what about the distance of zero or minus two from B, which is minus two three.
That gives you root of twenty nine as the distance.
Why is that.
So that's square root of two squared plus minus five squared.
Over here you have zero and all you have minus two.
So minus two.
Minus zero.
That's the same as minus two squared which is the same as two square.
Right.
And three minus minus two gives you five square or minus five if you minus two minus minus two, minus
two, minus three which is one and the same.
So you have two squared, plus five squared, that's twenty five plus four and hence the distance between
zero minus two and minus two comma three is root of twenty nine.
So you can see that this point is not at the same distance from Vertex and vertex B hence this is not
the circuit center.
All right, let's proceed to option B..
Over here you have one comma minus one right now.
What is the distance of this point from one comma four over here you have one and over here you have
one.
So one minus one is zero.
So that zero square and that's not to be considered.
And four minus minus one gives you five.
Right.
So that's five squared, which is twenty five to the distance is root of twenty five which is equal
to five.
Right.
Let me right that over here that zero plus five square and taking the root you get the distance as five.
All right.
Now what is the distance of this point from Vertex B over here you have minus two and then three.
Right.
You will find that this distance also is equal to five, right.
Why is that?
So you have root of four squared plus three square right over here you have three and minus one, two,
three minus minus one gives you four.
That's four square over here and minus two minus minus one gives you minus three, minus three square
and three square are the same.
So you have three square over here and root of four squared plus three square is equal to five.
All right.
Now what is the distance of this point from Vertex C, which is five comma two.
That's five minus one.
That's four.
So you have four square and two minus minus one.
That's three.
So you have three square root of four squared plus three square.
That's again equal to five.
Let me right that over here.
Right.
So you can see that this point that is one comma minus one, is that the same distance from Vertex A,
B and C.
And hence, this is the correct answer.
That is the circumstance of this triangle over here is one comma, minus one.
All right.
Now let's proceed and check the special case of it.
Right, angle triangle.