Question 1

如圖，坐標平面上有一$\Delta$ABC，且A、B、C的坐標為(3，4)、(0，4)、(3，0)，求$\Delta$ABC的外心坐標

Accepted Answer

($\frac{3}{2}$，4)

Answer

(2，2)

Answer

(3，1)

Answer

(4，$\frac{3}{2}$)

Question 2

已知$\Delta$ABC中，如果$\angle A=42^{\circ}$，當$\angle B$為幾度時，$\Delta$ABC的外心會落在三角形的外部？

Accepted Answer

$38^{\circ}$

Answer

$68^{\circ}$

Answer

$48^{\circ}$

Answer

$58^{\circ}$

Question 3

如圖，O為鈍角$\Delta$ABC的外心，若$\overline{AB}$ = $\overline{AC}$ = 10，$\overline{BC}$ = 16，求$\Delta$ABC的外接圓半徑

Accepted Answer

$\frac{25}{3}$

Answer

8

Answer

6

Answer

$\frac{21}{4}$

Question 4

$\Delta$ABC為鈍角三角形，已知I為內心，$\angle A=110^{\circ}$，求$\angle BIC$的度數

Accepted Answer

$145^{\circ}$

Answer

$120^{\circ}$

Answer

$130^{\circ}$

Answer

$135^{\circ}$

Question 5

在直角$\Delta$ABC中，$\overline{AB}$ = 15，$\overline{AC}$ = 8，$\overline{CB}$ = 17，且$\angle A=90^{\circ}$，求$\Delta$ABC內切圓面積為何？

Accepted Answer

9$\pi$

Answer

12$\pi$

Answer

8$\pi$

Answer

7$\pi$

Question 6

圖中的直角三角形，請問那一點最有可能是外接圓的圓心，那一點最有可能是內切圓的圓心？

Accepted Answer

外接圓圓心：B，內切圓圓心：C

Answer

外接圓圓心：C，內切圓圓心：D

Answer

外接圓圓心：A，內切圓圓心：D

Answer

外接圓圓心：A，內切圓圓心：B

Question 7

$\Delta$ABC中，F、E分別為$\overline{AB}$、$\overline{AC}$的中點，已知$\overline{BG}$ = 24，求$\overline{BE}$ = ？

Accepted Answer

36

Answer

12

Answer

48

Answer

30

Question 8

已知直角$\Delta$ABC兩股長$\overline{BC}$ = 3，$\overline{AB}$ = 4，G為$\Delta$ABC的重心，求重心G到$\overline{AC}$的距離為何？

Accepted Answer

$\frac{4}{5}$

Answer

1

Answer

$\frac{2}{3}$

Answer

$\frac{2}{5}$

Question 9

直角$\Delta$ABC中，$\angle C=90^{\circ}$，中線$\overline{AD}$、$\overline{BE}$相交於G點，若$\overline{AB}$ = 10，$\overline{BC}$ = 6，求四邊形GDCE的面積 = ？

Accepted Answer

8

Answer

16

Answer

24

Answer

12

Question 10

如圖，$\Delta$ABC三中線相交於G點，且$\overline{GA}$ = 20，$\overline{GB}$ = 18，$\overline{GC}$ = 14，求$\overline{AD}$ + $\overline{BE}$ + $\overline{CF}$ = ？

Accepted Answer

78

Answer

69

Answer

72

Answer

64

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