Even if the radius is not same it will be 90 deg. There is need for the figure in this question. I have the fig at (https://drive.google.com/file/d/0B2EDcEci0le6UEdzQjdCcFlTcUU/edit?usp=sharing)
Here`s the explanation:
Let O be the center of larger circle and O1 be the center of the smaller circle.
Now join AO and CO(both are the radii of larger circle).
Then join BO1 and CO1(both are the radii of smaller circle).
You will notice that :
ang.OAC = ang.OCA
similarly,
ang.O1BC = ang.O1CB
Now in triangle ACB ;
ang.ACB = 180 - (ang. CAB + ang. CBA) ---------------- (1)
But,
ang .CAB = ang . OAB - ang. OAC
=90 - ang . OAC
=90 - ang . ACO ----------------------------------------- (2)
Similarly,
ang. CBA = 90 - ang. BCO1-------------------------------- (3)
Substituting (2) and (3) in (1) we get,
ang. ACB = 180 - (90 - ang. ACO + 90 - ang. BCO1)
ang. ACB = 180 - (180 - ang. ACO - ang. BCO1)
ang. ACB = 180 - 180 + ang. ACO + ang. BCO1
ang. ACB = ang. ACO + ang. BCO1 ---------------------- (4)
But,
OCO1 is a straight line i.e;
ang. ACO + ang. ACB + ang. BCO1 = 180
ang. ACB = 180 - (ang. ACO + ang. BCO1) ------------ (5)
Substituting (4) to (5)
We get,
ang. ACB = 180 - ang. ACB
ang. ACB X 2 = 180
ang. ACB = 180/2 = 90 deg.---------------(ANSWER)
