00:01
So in this question you have given a circle and with center c, let's say center is c and ab is an arc, ab is n line segment and this is the triangle acb and this angle is theta angle.
00:22
So this is radius r.
00:24
So we need to find the central angle theta.
00:27
So we know that theta is equal to arc length upon radius.
00:39
So from here we can write theta is equal to arc length given here 5.
00:44
So 5 upon r.
00:47
So or we can write r is equal to 5 upon theta.
00:53
We have here two result.
00:54
Now in a triangle abc, angle a is theta, angle a theta.
01:05
So we can write from here that cos theta is equal to ac square plus bc square minus ab square whole upon 2ac into 2bc.
01:29
So after we know that here ac is equal to bc is radius of this circle.
01:38
So we can write here cos theta is equal to r square plus r square and minus we have given here the length of ab is 4 centimeters.
01:50
So from here we can write that is 16 upon 2r square.
01:56
So after solving this equation we have here r square cos theta is equal to r square minus 8 and let's say that is our equation number first.
02:10
Now we have here r is equal to 5 upon theta.
02:14
So now put the value of r...