如图,△ABC内接于⊙O,AD⊥BC于点D,AD=2cm,AB=4cm,AC=3cm,则⊙O的直径是_.
问题描述:
如图,△ABC内接于⊙O,AD⊥BC于点D,AD=2cm,AB=4cm,AC=3cm,则⊙O的直径是______.
答
作⊙O的直径AE,连CE,如图,
∵AE为直径,
∴∠ACE=90°,
又∵∠E=∠B,
∴Rt△AEC∽Rt△ABD,
∴
=AE AB
,AC AD
而AD=2cm,AB=4cm,AC=3cm,
∴AE=
=AB•AC AD
×4cm=6cm.3 2
所以⊙O的直径是6cm.
故答案为:6cm.