怎么解这道几何证明题---题 1. 如图, 过圆外一点 $P$ 作圆 $O$ 的切线 $PA$ 交圆与 $A$, 在圆上一点 $B$(不与 $A$ 重合), $PA=PB$, 点 $D$ 在优弧 $AB$ 上运动, 连接 $PD$ 与圆的另一个交点为 $C$. 过点 $B$ 做 $BH // AD$ 交 $PC$ 点 $H$, 过点 $H$ 做 $HK // BD$, 交直线 $AD$ 延长线点 $K$(不与 $K$ 重合). (1) 求证 $BD^2=AD \times KD$. **Chart Description:** * Type: Geometric diagram. * Main Elements: * A circle with center O. * Point P is located outside the circle. * Point A is on the circle, and PA is a tangent line segment to the circle at A. * Point B is on the circle, and it is distinct from A. A dashed line segment AB is drawn. * Point D is on the major arc AB of the circle. * Point C is on the circle, and it is the other intersection point of the line segment PD with the circle (distinct from D). Line segments PC, PD, CD are drawn. * Line segments PA, PB, AD, BD, AC, BC are drawn. * Point H is on the line segment PC. * Line segment BH is drawn, and it is parallel to line segment AD. * Line segment HK is drawn, and it is parallel to line segment BD. * Point K is on the extension of line AD. Point K is distinct from D. * Labels: Points P, A, B, C, D, H, K, O are labeled. O is labeled as the center of the circle. **Relationships shown:** * PA is tangent to the circle at A. * Points A, B, C, D are on the circle. * PA = PB is stated in the problem description. * D is on the major arc AB. * PD intersects the circle at C and D. * H is on PC. * BH is parallel to AD. * HK is parallel to BD. * K is on the extension of AD.