China Math Olympiad | Can you find the radius of the circle

Can you find the radius of the circle in any triangle ABC, if AB is A, AC is B, BC is C and this angle is theta, then C square, it is A square minus B square minus 2AB cos theta AC square, it will be AP square minus CP square minus 2 times AP times CP times cos 120 degrees and AC square, it is 3 square minus 2 square minus 2 times 3 times 2 and cos 120 degrees, it is minus 1 over 2 and 2 will get cancelled. So, AC square, it is 9 minus 144 minus 36 CP square minus 2 times BP times CP times cos 60 degrees and BC square, it is 4 square minus 2 square minus 2 times 4 times 2 and cos 60 degrees is 1 over 2 and 2 will get cancelled. So, BC square, it is 16 minus 144 minus 48 and BC square, it will be 160 minus 48. So, BC square, it will be 120 and now, suppose this angle is alpha, then inter angle ABC, BC square, it will be AB square minus AC square minus 2 times AB times AC times cos alpha and BC square is 112 and AB, it will be 3 minus 4, that will be 7 square minus 6 and AC square is 189 minus 2 times AB 7 and AC, it is root 189 times cos alpha and 112, it is 49 minus 189 minus 14 times and root 189, it is 3 times root 21 cos alpha and 112, it will be 238 minus 42 times root 21 cos alpha and 42 root 21 cos alpha, it will be 238 minus 112, that will be 126 and 42 times 3 is 126. So, cos alpha, it will be 3 over root 21 and sin alpha, it is root under 1 minus cos square alpha and it will be root under 1 minus 9 over 21 and it is root under 2 n over 21 and it is root under root 7 and in any triangle ABC, if BC is A, AC is B, ABC, then A over sin A, it is equal to B over sin B, it is equal to C over sin C, that will be 2 times radius of circum be 2 times radius of circum circle and BC, BC square, it is 102 n. So, BC, it will be 4 times root 7, BC, it is 4 times root 7 over sin alpha, it is 2 over root 7, it is 2 R and 2 times 2 is 4 and 2 will get cancelled. So, root 7 over 1 over root 7, it is R and it is root 7 times root 7, it is R and 7, it is R. So, radius, it will be 7.