Question 1

設兩圓的半徑為4、7，當兩圓交於相異兩點，則連心線段長可為下列何者？

Accepted Answer

9

Answer

3

Answer

12

Answer

2

Question 2

已知圓O的半徑為13公分，若弦$\overline{AB}$的弦心距為5公分，則$\overline{AB}$=？

Accepted Answer

24公分

Answer

12公分

Answer

16公分

Answer

8公分

Question 3

$\overline{AB}$切圓O於B，$\overline{AO}$交圓O於C，若$\overline{AB}$=12，$\overline{AC}$=8，則圓O之面積應為多少？

Accepted Answer

25$\pi$

Answer

100$\pi$

Answer

16$\pi$

Answer

9$\pi$

Question 4

圓外切四邊形ABCD中，$\overline{AB}$=2x+3、$\overline{BC}$=3x-5、$\overline{CD}$=2x+7、$\overline{AD}$=4x-3，則 x=？

Accepted Answer

6

Answer

7

Answer

5

Answer

8

Question 5

已知平面上有兩圓，其半徑分別為4公分與7公分，若兩圓的連心線段長為8公分，則兩圓有幾條內公切線？

Accepted Answer

0

Answer

2

Answer

3

Answer

1

Question 6

下列有關圓內接四邊形的敘述，何者錯誤？

Accepted Answer

圓內接平行四邊形必為正方形

Answer

圓內接四邊形的對角互補

Answer

圓內接四邊形的一個外角與其相鄰內角的對角相等

Answer

圓內接梯形的兩對角線長必相等

Question 7

直線AD切圓於A點，$\overline{AD}$//$\overline{BC}$，若$\angle CAD=55^{\circ}$，則$\angle CAB=$？

Accepted Answer

$70^{\circ}$

Answer

$60^{\circ}$

Answer

$50^{\circ}$

Answer

$80^{\circ}$

Question 8

$\overline{PA}$切圓O於A點，$\overline{PB}$切圓O於B點，C點在圓周上，若圓心角$\angle AOB=140^{\circ}$，則$\angle ACB + \angle APB=$？

Accepted Answer

$110^{\circ}$

Answer

$120^{\circ}$

Answer

$115^{\circ}$

Answer

$105^{\circ}$

Question 9

直線L切圓O於B點，已知$\angle OBA=70^{\circ}$，則$\angle 1 + \angle 2 = $？

Accepted Answer

$40^{\circ}$

Answer

$60^{\circ}$

Answer

$50^{\circ}$

Answer

$30^{\circ}$

Question 10

$\overline{AB}$切圓$O_1$於B點，$\overline{AC}$切圓$O_2$於C點，$\overline{BC}$分別交圓$O_1$、圓$O_2$於D、E兩點。若$\angle BO_1D=40^{\circ}$，$\angle CO_2E=60^{\circ}$，則$\angle A$的度數為何？

Accepted Answer

$130^{\circ}$

Answer

$100^{\circ}$

Answer

$120^{\circ}$

Answer

$140^{\circ}$

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