Question

Geometry question

Answer 1

prove that


\(\large \color{black}{\begin{align} PA\cdot PB=PC\cdot PD\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

\(\angle ADP\cong \angle CBP\) as they both intercept the same arc \(AC\)
\(\angle APD\cong \angle CPB\)

together imply \(\triangle ADP \sim \triangle CBP\) by \(AA\) similarity.
setting up proportion of corresponding sides gives the desired relation :
\[\dfrac{PA}{PC} = \dfrac{PD}{PB}\]

Answer 3

thanks