2. 选择题.
(1)如图,$AB是\odot O$的直径,若$\angle DBA = 55^{\circ}$,则$\angle BCD$的度数是()

A. $35^{\circ}$ B. $55^{\circ}$ C. $70^{\circ}$ D. $110^{\circ}$
(2)$\triangle ABC为\odot O$的内接三角形,若$\angle AOC = 160^{\circ}$,则$\angle ABC$的度数是()
A. $80^{\circ}$ B. $160^{\circ}$
C. $100^{\circ}$ D. $80^{\circ}或100^{\circ}$
(3)如图,$OA = OB = OC$,且$\angle ACB = 30^{\circ}$,则$\angle AOB$的度数是()

A. $40^{\circ}$ B. $50^{\circ}$ C. $60^{\circ}$ D. $70^{\circ}$
(4)如图,$AB$是半圆的直径,$D是\overset{\frown}{AC}$的中点,$\angle ABC = 50^{\circ}$,则$\angle DAB$的度数是()

A. $55^{\circ}$ B. $60^{\circ}$ C. $65^{\circ}$ D. $70^{\circ}$
(5)如图,$\odot C$过原点,且与两坐标轴分别交于点$A$,$B$,点$A的坐标为(0,3)$,$M是第三象限内\overset{\frown}{OB}$上一点,$\angle BMO = 120^{\circ}$,则$\odot C$的半径为()

A. $6$ B. $5$ C. $3$ D. $3\sqrt{2}$
(6)一个圆形人工湖如图所示,弦$AB$是湖上的一座桥,已知桥$AB的长为100\ m$,测得圆周角$\angle ACB = 45^{\circ}$,则这个人工湖的直径$AD$为()

A. $50\sqrt{2}\ m$ B. $100\sqrt{2}\ m$
C. $150\sqrt{2}\ m$ D. $200\sqrt{2}\ m$

2.
(1)A
(2)D
(3)C
(4)C
(5)C
(6)B

3. 如图,$AB是\odot O$的直径,点$C$,$D在\odot O$上,连接$CA$,$CB$,$DC$,$DB$.已知$\angle D = 30^{\circ}$,$BC = 3$,求$AB$的长.

3.解:$\because ∠D=30^{\circ },$
$\therefore ∠A=30^{\circ }.$
∵AB是$\odot O$的直径,
$\therefore ∠ACB=90^{\circ },$
$\therefore AB=2BC.$
$\because BC=3,$
$\therefore AB=6.$