Let's do this question, the radius of the circle is five centimeter, Ebe is five square root of three
centimeter.
Find AC this side over here if angle B AC is equal to angle A.B.C..
So these two angles are equal.
All right.
Pause the video, give it a try and then let's do it together.
All right.
Let's do it together.
These two angles are equal, right?
So Triangle ABC is forming an isosceles triangle.
Therefore AC has to be equal to B.C..
All right.
Now let's join it to all and be two.
OK, now or A and or B are radiuses therefore or HCB is a quite right because always equal will be and
AC is equal to c.B.
So we have two sets of adjacent sides being equal and OCB is a kite already.
Now let's join up and see, all right, now we know that a the bigger diagonal is the perpendicular
by sector of the shorter one.
Now, let me right the point of intersection aspy.
And in that case, we know AP is equal to B B and this angle over here, angle opihi will be equal to
90 degrees.
All right.
Now we know that the radius of the circle is five centimeter.
So all is equal to or be is equal to five centimeter.
Now we can find PBS Birute three divided by two.
Right.
B, B and B will be five to three by two because the longer diagonal is a big factor of the shorter
one.
So AP IB is the shorter one.
The AP and both of them are equal to fire three by two.
All right, now let's analyze triangle or B B triangle, OPB.
You will see the right angle triangle, right?
Because Angle opened 90 degrees, therefore OPIS Square is equal to Olby Square minus PBIS Square as
per Pythagoras's theorem.
Right, or B is the hypotenuse or B squares or B squared plus B square.
Or you can write or B square is equal to or B squared minus B square.
But that's five square minus Bierut, three by two the whole square.
And hence solving this you will get opis is equal to five divided by two.
All right.
Now let's draw a triangle up over here.
Now, we know this site, OPIS is Fabi two, obvious is five and PB's five by Route three.
Now, let's take a sign of this angle, Teater.
Now more of this you will learn in the section on trigonometry.
Now, SINTA is equal to the ratio of the length of the opposite side to the hypotenuse that is S.T.
in this case is equal to the opposite side of this angle is Beeby.
And the edges inside of the hypotenuse of this triangle is or will be assigned data is equal to be by
Olby.
Now SINTA is five by two or three divided by five.
That's equal to room three by two.
All right, now, when sign data is equal to rule three by two, it will be equal to 60 degree and hence
angle B or B is equal to 60 degrees.
You will see Àngel OCB is equal to anger OBC, these two angles are equal because Albe is equal to Ossy
because Obion OCR radiuses of this circle.
Right now this angle is 60 degrees and these two angles are equal.
Hence these two also have to be equal to 60 degrees.
Right.
That's why.
Why is that so this plus this plus this is 180.
If I said this is X, this is X then 60 plus two X is equal to 180 degree or X is equal to 60 degrees.
Right.
So Triangle OBC is an equilateral triangle.
So Triangle OBC we have found is an equilateral triangle where each angle is equal to sixty degrees.
Now we need to find AC and we have we know that it's easy to see now in this case because triangle obviously
is an equal triangle.
Every side will be equal and we know it will be equal to five centimeter.
Therefore B.C. is also equal to five centimeter and hence AC is equal to five centimeter.
And that is your answer.