A、B 和 C 是圆周上的点。 角 CAB = 角 CBA。 DA 和 DB 是从点 D 引向圆的切线。 证明三角形 ACD 和三角形 BCD 全等。 答案

1. Use the equal angles in triangle $ABC$ to identify an equal pair of sides.

In $\triangle ABC$,
$\angle CAB = \angle CBA.$
Hence the sides opposite these equal angles are equal:
$BC = AC.$

2. Use the tangent property to identify another equal pair of sides.

Since $DA$ and $DB$ are tangents to the circle from the same external point $D$,
$DA = DB.$

3. State the common side and conclude congruence.

The side $CD$ is common to both triangles, so
$CD = CD.$
Thus, in $\triangle ACD$ and $\triangle BCD$:
$AC = BC, \quad AD = BD, \quad CD = CD.$
Therefore,
$\triangle ACD \cong \triangle BCD \quad \text{(SSS)}.$