正弦定理a/sinA=b/sinB=c/sinC=2R
2R（sinA*sinA-sinC*sinC）=（根号2*a-b）*sinB
左右乘以2R并利用正弦定理化简得 a^2-c^2=根号2*ab-b^2
c^2=a^2+b^2-根号2*ab
而余弦定理c^2=a^2+b^2-2abcosC 根号2＝2cosC
C＝π/4 c=2RsinC=根号2*R 角AOB＝2角C＝π/2 设角BOC=α,则角AOC=3π/2-α
SΔABC=SΔAOB+SΔBOC+SΔAOC=1/2*R^2+1/2*R^2*sinBOC+1/2*R^2*sinAOC=1/2*R^2(1+sinα+sin(3π/2-α))=1/2*R^2(1+sinα-cosα)=1/2*R^2(1+根号2sin（α－π/4）)