Question 1

如圖，已知矩形ABCD中，$\overline{AB}$ = 6，$\overline{AD}$ = 8，以A點為圓心，r為半徑畫圓，若B、C、D三點中有一點在圓外，兩點在圓內，則半徑r的範圍為何？

Accepted Answer

8 < r< 10

Answer

10 < r< 12

Answer

5 < r< 6

Answer

6 < r< 8

Question 2

如圖，那一條直線是圓O的切線？

Accepted Answer

直線N

Answer

直線M

Answer

沒有任何切線

Answer

直線L

Question 3

已知圓的直徑為19公分，而圓心O到4條直線L、M、N、H的距離為19公分、10公分、9.5公分、7公分，則此4條直線中那一條是切線？

Accepted Answer

直線N

Answer

直線M

Answer

直線H

Answer

直線L

Question 4

如圖，$\overline{AB}$為圓上之一弦，$\overline{OM}$為其弦心距，若$\overline{AB}$ = 16，$\overline{OM}$ = 6，則圓O的面積為何？

Accepted Answer

100$\pi$

Answer

144$\pi$

Answer

96$\pi$

Answer

81$\pi$

Question 5

$\overline{OA}$、$\overline{OB}$、$\overline{OC}$為圓O的三弦心距，且$\overline{OA}$ = 3，$\overline{OB}$ = 4，$\overline{OC}$ = 5，則那條弦心距最長？

Accepted Answer

$\overline{A_1A_2}$

Answer

$\overline{B_1B_2}$

Answer

無法判斷

Answer

$\overline{C_1C_2}$

Question 6

如圖，圓O與正方形ABCD的兩邊$\overline{AB}$、$\overline{AD}$相切，且$\overline{DE}$與圓O相切於E點，若$\overline{DE}$ = 5，$\overline{OD}$ = $\sqrt{41}$，則正方形ABCD的邊長為何？

Accepted Answer

9

Answer

13

Answer

7

Answer

11

Question 7

如圖，$\overline{AB}$為圓的直徑，直線L與圓O相切於B點，C點在直線L上，已知圓O的半徑為15，$\overline{BC}$ = 16，則$\overline{AC}$ 的長度為何？

Accepted Answer

34

Answer

17

Answer

26

Answer

30

Question 8

如圖，P為圓O外一點，$\overline{PM}$與$\overline{PN}$為圓O的切線，M、N為切點，已知圓O的半徑為5公分，$\overline{OP}$ = 10公分，$\angle MOP=60^{\circ}$，則$\overline{MN}$ 為多少公分？

Accepted Answer

5$\sqrt{3}$

Answer

3$\sqrt{7}$

Answer

6$\sqrt{2}$

Answer

4$\sqrt{5}$

Question 9

設四邊形ABCD為圓O的圓外切四邊形，且$\overline{AD}$ = 6x - 8，$\overline{AB}$ = x + 8，$\overline{BC}$ = 2x - 1，$\overline{CD}$ = 3x + 3，則 x  = ？

Accepted Answer

5

Answer

4

Answer

6

Answer

2

Question 10

如圖，四邊形ABCD為等腰梯形，圓O為此梯形的內切圓，已知等腰梯形的周長為36，則等腰梯形的腰長為何？

Accepted Answer

9

Answer

15

Answer

12

Answer

18

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