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Students in this video, let's discuss how to find the sock'em center of a triangle if you know the

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three vertices of the triangle.

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All right.

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Now, remember, we have discussed what the Sock'Em Center is.

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It's the meeting point of the perpendicular bicyclers of the sides of the triangle.

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All right.

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Now, there is a special case where we can easily find the Starcom Center.

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That's the case of a right angle triangle.

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Right.

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We have learned something about this which will help us find the sock'em center of a right angle triangle

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very quickly now.

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We will discuss that later in this video.

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We are discussing the general case.

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All right.

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Now to find the sock'em center, you need to check which point among the four given options is at the

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same distance from every vertex of the triangle.

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Now, why is that?

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So, for example, you have Triangle ABC over here.

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Now, if this is the center of this triangle, then with this point as the center, you can draw a circle

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that will meet every vertex of the triangle.

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Right.

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We have discussed that.

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And this is called the Circle Circle of the Triangle.

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And this is called Issaka Radius right now.

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That's why the distance of this point from each of the vertices has to be equal.

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If this is all then or is the radius of the circle circle.

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Similarly, Albie's the radius of the circle circle and Ossy is the radius of that circle circle.

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All right.

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So let's proceed.

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Let me clear this up.

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OK, now say the four vertices that are given to you are zero comma, minus two one comma, minus one,

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two, comma one and two comma zero.

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Now, the approach should be that you need to find which among these four points is at the same distance

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from E, B and C..

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All right.

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Now, let's start with option one.

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What is the distance of zero comma, minus two from one comma for we know how to find the distance when

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we know the vertices of two points.

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Right.

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So you will get the answer.

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The square root of thirty seven.

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That is root of one square plus six square.

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Right.

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Why is that.

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So you have zero and you have one.

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So zero minus one gives you minus one and that's the same as one square.

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Right.

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And minus two.

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Minus four gives you minus six, minus X squared and six squared is the same.

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So you're right, six squared over here.

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So six squared plus one square gives you thirty seven and ends the distance between point eight.

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That's this vertex and this option is route 37.

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All right.

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Now what about the distance of zero or minus two from B, which is minus two three.

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That gives you root of twenty nine as the distance.

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Why is that.

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So that's square root of two squared plus minus five squared.

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Over here you have zero and all you have minus two.

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So minus two.

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Minus zero.

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That's the same as minus two squared which is the same as two square.

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Right.

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And three minus minus two gives you five square or minus five if you minus two minus minus two, minus

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two, minus three which is one and the same.

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So you have two squared, plus five squared, that's twenty five plus four and hence the distance between

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zero minus two and minus two comma three is root of twenty nine.

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So you can see that this point is not at the same distance from Vertex and vertex B hence this is not

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the circuit center.

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All right, let's proceed to option B..

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Over here you have one comma minus one right now.

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What is the distance of this point from one comma four over here you have one and over here you have

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one.

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So one minus one is zero.

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So that zero square and that's not to be considered.

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And four minus minus one gives you five.

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Right.

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So that's five squared, which is twenty five to the distance is root of twenty five which is equal

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to five.

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Right.

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Let me right that over here that zero plus five square and taking the root you get the distance as five.

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All right.

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Now what is the distance of this point from Vertex B over here you have minus two and then three.

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Right.

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You will find that this distance also is equal to five, right.

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Why is that?

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So you have root of four squared plus three square right over here you have three and minus one, two,

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three minus minus one gives you four.

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That's four square over here and minus two minus minus one gives you minus three, minus three square

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and three square are the same.

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So you have three square over here and root of four squared plus three square is equal to five.

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All right.

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Now what is the distance of this point from Vertex C, which is five comma two.

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That's five minus one.

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That's four.

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So you have four square and two minus minus one.

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That's three.

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So you have three square root of four squared plus three square.

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That's again equal to five.

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Let me right that over here.

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Right.

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So you can see that this point that is one comma minus one, is that the same distance from Vertex A,

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B and C.

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And hence, this is the correct answer.

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That is the circumstance of this triangle over here is one comma, minus one.

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All right.

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Now let's proceed and check the special case of it.

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Right, angle triangle.