Let's do this question.
ABC is a triangle or is a point at equal distance that's 10 centimeter from A, B and C and it's in
the plain of ABC.
All right.
Angle A, 60 degree angle B, 60 degree find ABC.
Now, pause the video, give it a try and then let's do it together.
All right.
Let's do it together.
Over here.
You have triangle ABC, right.
And it's mentioned that always a point, which is equidistant from A, B and C now.
Therefore, always the sock'em center of this triangle.
Right.
Why?
Because all is equal to Albie's equal or C so you can draw a circle that touches A, B and C, right.
Therefore or is this Sock'Em Center.
All right.
Now it's given that a 60 degree and B 60 degree.
Therefore Anglesey also will be 60 degrees and that means A.B.C. Triangle.
ABC is an equilateral triangle.
All right, now let me join up to a BNC.
OK, so basically we need to find the side of this equilateral triangle.
All right, now let me draw the circle circle, OK?
Now let me extend it or such that it meets B.C. at point B.
OK, now this point over here will make it right angle with B, C.
Why is that so?
Because in an equilateral triangle, if you remember the median.
The perpendicular biosecure.
The altitude.
And the angle sector.
All are the same line, right to all here AP is the median.
It's also the perpendicular bisected of side B.C. It's also the altitude through Vertex and it is also
the angle by sector of angle.
Right.
So we have already covered that.
So let me assume that you know this and let us proceed.
So what is it that we have done?
We have dropped a perpendicular from all to B C and that's meeting B, C at point B.
Now you can see that angle B all be over here will be equal to Angle S.O.P.
Why will they be equal.
Can you tell me that, Bobby, this angle over here will be equal to this angle over here?
They will be equal because if you take Triangle Bobby, that's triangle B or B and Triangle S.O.P.
You will see that these two are congruent, why you have a right angle over here and you have a right
angle over here.
Now, Olby will be equal to Orsi because they are both radii of this Hachem circle.
Right.
And OPIS is a common sight.
Right.
Therefore, as per artist congruence criteria, these two triangles are congruent and hence angle B
or B is equal to an S.O.P.
Now you can see that that will be equal to 60 degrees.
Let me make some space over here.
All right, now each of these angles will be equal to 60 degrees.
Now, why is that?
These are 60 degrees over here.
Below is the angle by sector of B, right.
Because we have seen that the angle by sector median, but perpendicular by sector and altitude are
all the same line for the equilateral triangle or here and will be a 60 angle.
All BP will be 60 by two.
That's thirty degrees.
Right.
And you have a 90 degree angle over here.
Therefore angle BOPE will be 180 minus 90, minus 30.
That's equal to 60 degree.
Similarly, angle S.O.P will also be equal to 60 degrees.
Now let's take sine 60.
That would be BP divided by B or right in triangle BP.
Or if you take sine 60, that would be BP divided by B, right.
All right, so that's opposite side, divided by hypotenuse, that's triangle B, B, or now sine 60,
we know is equal to rule three, divided by two.
All right, now it's given that the distance of all from the vortex is 10 centimeters to be or will
be equal to 10 centimeters right now.
Therefore, let's solve it.
We get BP divided by 10 is equal to room three by two.
Or you can solve BP's five three.
Now, if option is five to three, Donmar, the answer is five to three.
Right.
Because what is asked, we need to find B, c.
Now, BC is equal to Piru trying to do that's equal to 10 Rotary.
Why is that so?
Because BP and B.C. are corresponding sites of two congruent triangles.
Therefore, B.C. is equal to two times five in the rule three, that's 10 rule three, and that is the
answer to this question.