The diagram, not drawn to scale, shows two concentric circles, centre $O$ .
$AB$ and $AD$ are tangents to the smaller circle at $B$ and $D$ respectively, centre $O$ .
$AC$ is the diameter of the larger circle. (a) Show that triangle $ABC$ is congruent to triangle $ADC$ .
Give a reason for each statement you make.

Worked solution

1. 得出 AB 与 AD 相等并给出几何依据

$AB = AD$ （从圆外一点向圆引出的两条切线长相等）。

2. 得出角 BAC 与角 DAC 相等并给出几何依据

$\angle BAC = \angle DAC$ （连接圆外一点与圆心的线段平分两条切线间的夹角，且 $AC$ 为直径经过圆心 $O$ ）。

3. 结合公共边应用 SAS 判定三角形全等

$AC = AC$ （公共边）。
由 SAS（边角边）判定定理可得 $\triangle ABC \cong \triangle ADC$ 。

Answer

在 $\triangle ABC$ 和 $\triangle ADC$ 中：

因此，根据 SAS（边角边）全等判定定理， $\triangle ABC \cong \triangle ADC$ 。

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