Question

圆O是△ABC的外接圆,△ABC是钝角三角形,且 AB=AC=6,BC=8,圆O的周长是多少?

Answer 1

如图所示

连结AO并延长交圆O于E,AE交BC于D

∵AB=AC=6,

∴AE⊥BC

∵∠BAE=∠DAB

∠ABE=∠BDA=90°

∴△ABE∽△ADB

∴AB/AE=AD/AB

∵AB=AC=6,BC=8

∴AD=2√5

∴AE=(18/5)√5

圆O的周长=πAB=(18π/5)√5