Given three points a, B and C, according to the following conditions, can a, B and C determine a circle? If you can, request the radius; if you can't, please explain the reason. (1) AB = [63 + 4] cm, BC = 123cm, AC = [63-4] cm; (2) AB = AC = 10cm, BC = 12cm

Given three points a, B and C, according to the following conditions, can a, B and C determine a circle? If you can, request the radius; if you can't, please explain the reason. (1) AB = [63 + 4] cm, BC = 123cm, AC = [63-4] cm; (2) AB = AC = 10cm, BC = 12cm

(1) ∵ 63 + 4 + 63-4 = 123, ∵ AB + AC = BC, ∵ three points a, B and C are collinear, ∵ a circle can not be determined; (2) ∵ 10 + 10 = 20 ＞ 12, ∵ three points a, B and C are not collinear, ∵ a circle can be determined; through a, ad ⊥ BC, Bo, ∵ BC = 12, ∵ DB = 6, ∵ AB = 10, ∵ ad = 102 − 62 = 8, OB = x